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• Radical Functions and Equations Maintaining Mathematical Proficiency – Page 541
• Radical Functions and Equations Mathematical Practices – Page 542
• Lesson 10.1 Graphing Foursquare Root Functions – Page(543-550)
• Graphing Square Root Functions 10.1 Exercises – Folio(548-550)
• Lesson 10.two Graphing Cube Roots Functions – Page(551-556)
• Graphing Cube Roots Functions ten.2 Exercises – Page(555-556)
• Radical Functions and Equations Written report Skills: Making Note Cards – Page 557
• Study Skills: Making Note Cards
• Radical Functions and Equations 10.1–ten.two Quiz – Page 558
• Lesson 10.3 Solving Radical Equations – Folio(559-566)
• Solving Radical Equations ten.3 Exercises – Page(564-566)
• Lesson 10.4 Inverse of a Part – Page(567-574)
• Inverse of a Office x.4 Exercises – Page(572-574)
• Radical Functions and Equations Functioning Task: Medication and the Mosteller Formula – Folio 575
• Radical Functions and Equations Chapter Review – Folio (576-578)
• Radical Functions and Equations Affiliate Examination – Page 579
• Radical Functions and Equations Cumulative Cess – Folio(580-581)

Radical Functions and Equations Maintaining Mathematical Proficiency

Evaluate the expression.
Question 1.
7\(\sqrt{25}\) + 10
Answer:

Question 2.
-8 – \(\sqrt{\frac{64}{16}}\)
Reply:

Question 3.
\(5\left(\frac{\sqrt{81}}{3}-seven\right)\)
Respond:

Question 4.
-2(3\(\sqrt{9}\) + 13)
Answer:

Graph f and g. Describe the transformations from the graph of f to the graph of one thousand.
Question 5.
f(x) = x; g(x) = 2x – 2
Answer:

Question half-dozen.
f(x) = x; thousand(x) = \(\frac{one}{iii}\)x + 5
Answer:

Question 7.
f(10) = ten; g(x) = -x + iii
Answer:

Question 8.
Abstract REASONING
Let a and b represent constants, where b ≥ 0. Draw the transformations from the graph of m(x) = ax + b to the graph of n(x) = -2ax – 4b.
Reply:

Radical Functions and Equations Mathematical Practices

Mathematically adept students distinguish correct reasoning from flawed reasoning.

Monitoring Progress

Question one.
Which of the following square roots are rational numbers? Explain your reasoning.
\(\sqrt{0}, \sqrt{one}, \sqrt{3}, \sqrt{four}, \sqrt{five}, \sqrt{half dozen}, \sqrt{7}, \sqrt{8}, \sqrt{ix}\)
Respond:

Question 2.
The sequence of steps shown appears to prove that 1 = 0. What is wrong with this argument?

Answer:

Lesson 10.1 Graphing Square Root Functions

Essential Question What are some of the characteristics of the graph of a square root function?

EXPLORATION 1

Graphing Square Root Functions
Work with a partner.

• Make a table of values for each function.
• Apply the tabular array to sketch the graph of each role.
• Describe the domain of each function.
• Draw the range of each function.

Answer:

EXPLORATION two

Writing Square Root Functions
Work with a partner. Write a square root function, y = f (10), that has the given values. Then use the part to complete the table.

Answer:

Communicate Your Reply

Question 3.
What are some of the characteristics of the graph of a square root function?
Reply:

Question 4.
Graph each role. Then compare the graph to the graph of f(x) = \(\sqrt{x}\).
a. one thousand(ten) = \(\sqrt{x-i}\)
b. g(x) = \(\sqrt{x-1}\)
c. g(x) = ii\(\sqrt{x}\)
d. g(10) = -2 \(\sqrt{ten}\)
Respond:

Monitoring Progress

Describe the domain of the function.
Question 1.
f(x) = 10 \(\sqrt{ten}\)
Answer:

Question 2.
y = \(\sqrt{2x}\) + seven
Answer:

Question 3.
h(x) = \(\sqrt{-ten+1}\)
Answer:

Graph the function. Draw the range.
Question 4.
g(x) = \(\sqrt{ten}\) – iv
Respond:

Question 5.
y = \(\sqrt{2x}\) + 5
Reply:

Question 6.
north(ten) = 5\(\sqrt{x}\)
Answer:

Graph the function. Compare the graph to the graph of f(x) = \(\sqrt{10}\) .
Question vii.
h(x) = \(\sqrt{\frac{1}{4} ten}\)
Reply:

Question 8.
g(x) = \(\sqrt{x}\) – 6
Answer:

Question 9.
m(x) = -iii\(\sqrt{ten}\)
Respond:

Question 10.
Let g(x) = \(\frac{1}{2} \sqrt{x+4}+1\). Describe the transformations from the graph of f(x) = \(\sqrt{x}\) to the graph of g. Then graph g.
Answer:

Question 11.
In Case v, compare the velocities past finding and interpreting their average rates of change over the interval d = thirty to d = xl.
Answer:

Question 12.
WHAT IF?
At what depth does the velocity of the seismic sea wave exceed 100 meters per 2nd?
Reply:

Graphing Square Root Functions 10.1 Exercises

Vocabulary and Core Concept Check

Question i.
COMPLETE THE Judgement
A ________ is a function that contains a radical expression with the contained variable in the radicand.
Answer:

Question two.
VOCABULARY
Is y = 2x\(\sqrt{5}\) a square root part? Explain.
Answer:

Question 3.
WRITING
How practice you describe the domain of a square root function?
Answer:

Question 4.
REASONING
Is the graph of k(x) = one.25\(\sqrt{ten}\) a vertical stretch or a vertical compress of the graph of f(x) = \(\sqrt{ten}\)? Explain.
Answer:

Monitoring Progress and Modeling with Mathematics

In Exercises 5–14, describe the domain of the function.
Question 5.
y = eight\(\sqrt{x}\)
Answer:

Question 6.
y = \(\sqrt{4x}\)
Answer:

Question 7.
y = 4 + \(\sqrt{-x}\)
Answer:

Question 8.
y = \(\sqrt{-\frac{i}{2^{x}}}\) + 1
Answer:

Question ix.
h(x) = \(\sqrt{ten-4}\)
Answer:

Question 10.
p(10) = \(\sqrt{x+7}\)
Answer:

Question 11.
f(10) = \(\sqrt{-x+8}\)
Answer:

Question 12.
g(x) = \(\sqrt{-x-1}\)
Answer:

Question 13.
one thousand(10) = 2\(\sqrt{x+four}\)
Respond:

Question fourteen.
n(x) = \(\frac{1}{two} \sqrt{-ten}-2\)
Answer:

In Exercises 15–xviii, match the role with its graph. Describe the range.
Question 15.
y = \(\sqrt{x-three}\)
Answer:

Question 16.
y = 3\(\sqrt{x}\)
Respond:

Question 17.
y = \(\sqrt{x}\) – 3
Answer:

Question 18.
y = \(\sqrt{-x+3}\)
Reply:

In Exercises 19–26, graph the function. Describe the range.
Question 19.
y = \(\sqrt{3x}\)
Answer:

Question 20.
y = four\(\sqrt{-x}\)
Answer:

Question 21.
y = \(\sqrt{x}\) + 5
Respond:

Question 22.
y = -two + \(\sqrt{x}\)
Respond:

Question 23.
f(x) = – \(\sqrt{x-3}\)
Answer:

Question 24.
g(x) = \(\sqrt{x+4}\)
Answer:

Question 25.
h(x) = \(\sqrt{ten+2}\) – 2
Answer:

Question 26.
f(x) = –\(\sqrt{ten-i}\) + three
Answer:

In Exercises 27–34, graph the role. Compare the graph to the graph of f (x) = \(\sqrt{x}\).
Question 27.
1000(10) = \(\frac{1}{four} \sqrt{x}\)
Answer:

Question 28.
r(x) = \(\sqrt{2x}\)
Answer:

Question 29.
h(x) = \(\sqrt{x+3}\)
Answer:

Question xxx.
q(x) = \(\sqrt{x}\) + eight
Respond:

Question 31.
p(x) = \(\sqrt{-\frac{1}{3} x}\)x
Answer:

Question 32.
g(ten) = -5\(\sqrt{x}\)
Reply:

Question 33.
m(x) = –\(\sqrt{x}\) – 6
Answer:

Question 34.
n(10) = –\(\sqrt{x}\) – 4
Answer:

Question 35.
ERROR ANALYSIS
Depict and right the mistake in graphing the function y = \(\sqrt{x}\) + one .

Answer:

Question 36.
Mistake Analysis
Describe and right the error in comparing the graph of g(x) = \(-\frac{one}{4} \sqrt{x}\) to the graph of f (ten) = \(\sqrt{x}\).

Answer:

In Exercises 37–44, draw the transformations from the graph of f (x) = \(\sqrt{x}\) to the graph of h. Then graph h.
Question 37.
h(ten) = 4\(\sqrt{x+two}\) – one
Respond:

Question 38.
h(10) = \(\frac{1}{2} \sqrt{x-6}\)+ 3
Answer:

Question 39.
h(ten) = 2\(\sqrt{-x}\) – vi
Reply:

Question 40.
h(x) = –\(\sqrt{ten-iii}\) – 2
Answer:

Question 41.
h(ten) = \(\frac{i}{iii} \sqrt{x+3}\) + 3
Respond:

Question 42.
h(x) = ii\(\sqrt{x-one}\) + 4
Answer:

Question 43.
h(ten) = -2\(\sqrt{x-one}\) + 5
Answer:

Question 44.
h(ten) = -five\(\sqrt{x+2}\) – ane
Answer:

Question 45.
COMPARING FUNCTIONS
The model South(d ) = \(\sqrt{30df}\) represents the speed S (in miles per 60 minutes) of a van earlier it skids to a finish, where f is the drag cistron of the road surface and d is the length (in anxiety) of the skid marks. The elevate factor of Road Surface A is 0.75. The graph shows the speed of the van on Road Surface B. Compare the speeds by finding and interpreting their average rates of change over the interval d = 0 to d = xv.

Answer:

Question 46.
COMPARING FUNCTIONS
The velocity v (in meters per second) of an object in motion is given by 5(E ) = \(\sqrt{\frac{2 Eastward}{grand}}\), where E is the kinetic free energy of the object (in joules) and m is the mass of the object (in kilograms). The mass of Object A is 4 kilograms. The graph shows the velocity of Object B. Compare the velocities of the objects by finding and interpreting the average rates of alter over the interval Due east = 0 to E = vi.

Answer:

Question 47.
Open-Ended
Consider the graph of y = \(\sqrt{x}\).
a. Write a part that is a vertical translation of the graph of y = \(\sqrt{ten}\).
b. Write a function that is a reflection of the graph of y = \(\sqrt{x}\).
Answer:

Question 48.
REASONING
Can the domain of a foursquare root office include negative numbers? Can the range include negative numbers? Explicate your reasoning.
Answer:

Question 49.
Trouble SOLVING
The nozzle force per unit area of a burn hose allows firefighters to control the corporeality of water they spray on a fire. The flow rate f(in gallons per infinitesimal) can be modeled past the office f = 12\(\sqrt{p}\), where p is the nozzle force per unit area (in pounds per square inch).

a. Apply a graphing calculator to graph the function. At what pressure does the flow rate exceed 300 gallons per minute?
b. What happens to the boilerplate rate of modify of the flow rate as the pressure increases?
Answer:

Question 50
PROBLEM SOLVING
The speed south (in meters per second) of a long jumper before jumping can be modeled past the function southward = ten.9\(\sqrt{h}\), where h is the maximum height (in meters from the footing) of the jumper.

a. Employ a graphing calculator to graph the part. A jumper is running ix.2 meters per second. Estimate the maximum top of the jumper.
b. Suppose the runway and pit are raised on a platform slightly college than the basis. How would the graph of the function be transformed?
Answer:

Question 51.
MATHEMATICAL CONNECTIONS
The radius r of a circle is given by r = \(\sqrt{\frac{A}{\pi}}\), where A is the area of the circumvolve.

a. Describe the domain of the function. Use a graphing reckoner to graph the function.
b. Use the trace characteristic to approximate the area of a circle with a radius of 5.4 inches.
Answer:

Question 52.
REASONING
Consider the function f(x) = 8a\(\sqrt{ten}\).
a. For what value of a will the graph of f exist identical to the graph of the parent square root function?
b. For what values of a will the graph of f exist a vertical stretch of the graph of the parent foursquare root function?
c. For what values of a will the graph of f be a vertical compress and a reflection of the graph of the parent square root role?
Reply:

Question 53.
REASONING
The graph represents the function f(x) = \(\sqrt{ten}\).

a. What is the minimum value of the office?
b. Does the part have a maximum value? Explain.
c. Write a square root function that has a maximum value. Does the office have a minimum value? Explain.
d. Write a square root role that has a minimum value of -4.
Respond:

Question 54.
HOW Exercise YOU SEE IT?
Friction match each office with its graph. Explain your reasoning.

Answer:

Question 55.
REASONING
Without graphing, determine which role'south graph rises more steeply, f(x) = 5\(\sqrt{x}\) or g(x) = \(\sqrt{5x}\). Explain your reasoning.
Answer:

Question 56.
THOUGHT PROVOKING
Use a graphical approach to find the solutions of ten – 1 = \(\sqrt{5x-ix}\). Prove your work. Verify your solutions algebraically.
Answer:

Question 57.
Open-ENDED
Write a radical function that has a domain of all real numbers greater than or equal to -5 and a range of all real numbers less than or equal to 3.
Answer:

Maintaining Mathematical Proficiency

Evaluate the expression.(Section 6.2)
Question 58.
\(\sqrt [ 3]{ 343 }\)
Answer:

Question 59.
\(\sqrt [ iii]{ -64 }\)
Answer:

Question 60.
\(-\sqrt[3]{-\frac{1}{27}}\)
Reply:

Factor the polynomial.(Section 7.5)
Question 61.
xⁱⁱ + 7x + half-dozen
Answer:

Question 62.
dⁱⁱ – 11d + 28
Respond:

Question 63.
y² – 3y – forty
Answer:

Lesson 10.2 Graphing Cube Roots Functions

Essential Question What are some of the characteristics of the graph of a cube root part?

EXPLORATION one

Graphing Cube Root Functions
Work with a partner.

•  Brand a tabular array of values for each function. Use positive and negative values of x.
• Utilise the table to sketch the graph of each function.• Depict the domain of each function.
• Draw the range of each office.

Respond:

EXPLORATION 2

Writing Cube Root Functions
Piece of work with a partner. Write a cube root office, y = f(x), that has the given values. Then apply the function to complete the tabular array.

Respond:

Communicate Your Answer

Question iii.
What are some of the characteristics of the graph of a cube root role?
Respond:

Question 4.
Graph each part. Then compare the graph to the graph of f (10) = \(\sqrt [ three]{ x }\) .
a. 1000(x) = \(\sqrt [ three]{ x-ane }\)
b. g(x) = \(\sqrt [ iii]{ x-one }\)
c. g(ten) = 2 \(\sqrt [ 3]{ x }\)
d. k(x) = -2\(\sqrt [ iii]{ 10 }\)
Answer:

Monitoring Progress

Graph the function. Compare the graph to the graph of f(ten) = \(\sqrt [ iii]{ 10 }\).
Question i.
h(x) = \(\sqrt [ 3]{ x }\) + 3
Answer:

Question ii.
m(ten) = \(\sqrt [ iii]{ x }\) – 5
Answer:

Question 3.
m(ten) = four\(\sqrt [ 3]{ x }\)
Answer:

Graph the function. Compare the graph to the graph of f(ten) = \(\sqrt [ 3]{ x }\).
Question 4.
1000(ten) =\(\sqrt [three]{ 0.5x+5 }\) + five
Answer:

Question v.
h(x) = 4\(\sqrt [3]{ ten }\) – 1
Respond:

Question vi.
due north(ten) = \(\sqrt [ 3]{ four-10 }\)
Respond:

Question seven.
Allow thousand(ten) = \(-\frac{one}{2} \sqrt[iii]{x+2}\) – iv. Describe the transformations from the graph of f (x) = \(\sqrt [ three]{ ten }\) to the graph of chiliad. And so graph g.
Answer:

Question 8.
In Instance 4, compare the average rates of change over the interval x = 2 to x = ten.
Respond:

Question 9.
WHAT IF?
Estimate the historic period of an elephant whose shoulder height is 175 centimeters.
Reply:

Graphing Cube Roots Functions 10.2 Exercises

Vocabulary and Cadre Concept Bank check

Question 1.
Complete THE Sentence
The __________ of the radical in a cube root part is 3.
Answer:

Question 2.
WRITING
Describe the domain and range of the role f(ten) = \(\sqrt [3]{ x-4 }\) + ane.
Answer:

Monitoring Progress and Modeling with Mathematics

In Exercises 3–half-dozen, match the role with its graph.
Question 3.
y = 3\(\sqrt [3]{ x+2 }\)
Reply:

Question 4.
y = 3\(\sqrt [iii]{ x-2 }\)
Answer:

Question v.
y = 3\(\sqrt [iii]{ x+2 }\)
Answer:

Question vi.
y = \(\sqrt [3]{ x }\) – 2
Reply:

In Exercises seven–12, graph the function. Compare the graph to the graph of f(x) = \(\sqrt [ iii]{ x }\).
Question seven.
h(x) = \(\sqrt [3]{ x-4 }\)
Answer:

Question viii.
1000(ten) = \(\sqrt [3]{ x+1 }\)
Reply:

Question 9.
grand(x) = \(\sqrt [3]{ x+5 }\)
Answer:

Question x.
q(x) = \(\sqrt [3]{ 10 }\) – iii
Answer:

Question 11.
p(10) = 6\(\sqrt [iii]{ 10 }\)
Answer:

Question 12.
j(ten) = \(\sqrt[3]{\frac{i}{2} 10}\)
Answer:

In Exercises 13–16, compare the graphs. Find the value of h, m, or a.
Question 13.

Answer:

Question 14.

Answer:

Question xv.

Answer:

Question sixteen.

Answer:

In Exercises 17–26, graph the role. Compare the graph to the graph of f(x) = \(\sqrt [3]{ x }\).
Question 17.
r(10) = – \(\sqrt [3]{ x-2 }\)
Answer:

Question 18.
h(x) = – 3\(\sqrt [3]{ x+3 }\)
Answer:

Question 19.
k(x) = 5\(\sqrt [3]{ x+one }\)
Respond:

Question 20.
j(x) = 0.5\(\sqrt [three]{ ten-4 }\)
Answer:

Question 21.
g(x) = 4\(\sqrt [3]{ ten }\) – three
Answer:

Question 22.
g(x) = 3\(\sqrt [3]{ x }\) + 7
Answer:

Question 23.
n(x) = \(\sqrt [3]{ -8x }\) – 1
Answer:

Question 24.
five(x) =\(\sqrt [3]{ 5x }\) + 2
Answer:

Question 25.
q(x) = \(\sqrt[iii]{2(x+iii)}\)
Reply:

Question 26.
p(x) = \(\sqrt[3]{three(1-ten)}\)
Respond:

In Exercises 27–32, depict the transformations from the graph of f(ten) = \(\sqrt [three]{ x }\) to the graph of the given role. Then graph the given function.
Question 27.
g(x) = \(\sqrt [iii]{ x-4 }\) + 2
Answer:

Question 28.
northward(ten) = \(\sqrt [3]{ x+1 }\) – 3
Reply:

Question 29.
j(10) = -5\(\sqrt [3]{ x+3 }\) + 2
Answer:

Question xxx.
k(x) = half-dozen\(\sqrt [iii]{ x-9 }\) – five
Reply:

Question 31.
v(x) = \(\frac{1}{3} \sqrt[3]{x-i}\) + vii
Reply:

Question 32.
h(x) = -\frac{three}{2} \sqrt[3]{x+4} – 3
Answer:

Question 33.
ERROR Assay
Describe and correct the fault in graphing the function f(ten) = \(\sqrt [3]{ 10-three }\).

Answer:

Question 34.
ERROR ANALYSIS
Describe and correct the fault in graphing the part h(x) = \(\sqrt [3]{ ten }\) + 1.

Answer:

Question 35.
COMPARING FUNCTIONS
The graph of cube root role q is shown. Compare the average rate of change of q to the average rate of modify of f(10) = 3\(\sqrt [3]{ x }\) over the interval x = 0 to 10 = 6.

Answer:

Question 36.
COMPARING FUNCTIONS
The graphs of two cube root functions are shown. Compare the average rates of modify of the 2 functions over the interval x = -2 to x = 2.

Respond:

Question 37.
MODELING WITH MATHEMATICS
For a drag race automobile that weighs 1600 kilograms, the velocity v (in kilometers per hr) reached by the end of a drag race tin be modeled by the function 5 = 23.8\(\sqrt [three]{ p }\), where p is the car's power (in horsepower). Utilise a graphing calculator to graph the function. Estimate the power of a 1600-kilogram car that reaches a velocity of 220 kilometers per hour.
Answer:

Question 38.
MODELING WITH MATHEMATICS
The radius r of a sphere is given past the function r = \(\sqrt[3]{\frac{iii}{four \pi}} 5\), where V is the book of the sphere. Use a graphing computer to graph the function. Estimate the volume of a spherical embankment ball with a radius of 13 inches.
Answer:

Question 39.
MAKING AN Statement
Your friend says that all cube root functions are odd functions. Is your friend correct? Explain.
Answer:

Question 40.
HOW Do You lot SEE IT?
The graph represents the cube root office f(x) = \(\sqrt [three]{ 10 }\).

a. On what interval is f negative? positive?
b. On what interval, if whatsoever, is f decreasing? increasing?
c. Does f have a maximum or minimum value? Explicate.
d. Find the average charge per unit of alter of f over the interval 10 = -1 to 10 = i.
Answer:

Question 41.
Problem SOLVING
Write a cube root role that passes through the point (3, 4) and has an boilerplate rate of alter of -one over the interval ten = -5 to x = 2.
Answer:

Question 42.
Idea PROVOKING
Write the cube root part represented past the graph. Use a graphing calculator to check your answer.

Respond:

Maintaining Mathematical Proficiency

Factor the polynomial.(Section 7.6)
Question 43.
3x² + 12x – 36
Answer:

Question 44.
2xⁱⁱ – 11x + ix
Respond:

Question 45.
4x² + 7x – 15
Answer:

Solve the equation using square roots.(Department 9.3)
Question 46.
x² – 36 = 0
Answer:

Question 47.
5x² + 20 = 0
Answer:

Question 48.
(x + iv)² – 81
Reply:

Question 49.
25(x – 2)² = 9
Answer:

Radical Functions and Equations Study Skills: Making Note Cards

10.1–x.2 What Did YouLearn?

Core Vocabulary
square root function, p. 544
radical function, p. 545
cube root function, p. 552

Core Concepts
Lesson 10.1
Square Root Functions, p. 544
Transformations of Square Root Functions, p. 545
Comparing Square Root Functions Using Average Rates of Change, p. 546

Lesson 10.2
Cube Root Functions, p. 552
Comparison Cube Root Functions
Using Average Rates of Modify, p. 554

Mathematical Practices

Question one.
In Exercise 45 on page 549, what data are y'all given? What relationships are nowadays? What is your goal?
Answer:

Question ii.
What units of mensurate did you apply in your answer to Practise 38 on folio 556? Explain your reasoning.
Answer:

Study Skills: Making Note Cards

Invest in three different colors of notation cards. Utilize one colour for each of the post-obit: vocabulary words, rules, and calculator keystrokes.

• Using the outset color of note cards, write a vocabulary give-and-take on one side of a carte du jour. On the other side, write the definition and an example. If possible, put the definition in your own words.
• Using the second color of note cards, write a rule on ane side of a card. On the other side, write an caption and an instance.
• Using the tertiary colour of note cards, write a calculation on one side of a card. On the other side, write the keystrokes required to perform the calculation.
  Utilize the note cards as references while completing your homework. Quiz yourself once a day.
  

Radical Functions and Equations 10.one–10.two Quiz

Draw the domain of the part.(Lesson ten.1)
Question 1.
y = \(\sqrt{10-iii}\)
Reply:

Question 2.
f(10) = 15\(\sqrt{10}\)
Answer:

Question three.
y = \(\sqrt{iii-ten}\)
Answer:

Graph the function. Describe the range. Compare the graph to the graph of f(x) = \(\sqrt{ten}\). (Lesson 10.1)
Question four.
g(x) = \(\sqrt{x}\) + 5
Answer:

Question 5.
n(x) = \(\sqrt{x-4}\)
Answer:

Question half-dozen.
r(10) = –\(\sqrt{10-one}\) + 1
Answer:

Graph the function. Compare the graph to the graph of f(x) = \(\sqrt [3]{ x }\). (Lesson 10.2)
Question vii.
b(x) = \(\sqrt [iii]{ x+2 }\)
Answer:

Question 8.
h(10) = -3\(\sqrt [3]{ x-6 }\)
Answer:

Question ix.
q(x) = \(\sqrt [3]{ -iv-x }\)
Answer:

Compare the graphs. Find the value of h, m, or a. (Lesson x.1 and Lesson 10.ii)
Question ten.

Respond:

Question eleven.

Answer:

Question 12.

Answer:

Depict the transformations from the graph of f to the graph of h. And then graph h. (Department 10.1 and Section 10.two)
Question 13.
f(x) = \(\sqrt{10}\); h(x) = -3 \(\sqrt{x+2}\) + 6
Reply:

Question 14.
f(x) = \(\sqrt[3]{10}\); h(10) = \(\frac{i}{two} \sqrt[three]{10}-three\)
Answer:

Question fifteen.
The time t (in seconds) it takes a dropped object to fall h feet is given by t = \(\frac{1}{4} \sqrt{h}\). (Section x.i)

a. Use a graphing calculator to graph the function. Depict the domain and range.
b. It takes well-nigh vii.4 seconds for a stone dropped from the New River Gorge Bridge in West Virginia to reach the water beneath. About how high is the bridge above the New River?
Answer:

Question 16.
The radius r of a sphere is given by the part r = \(\sqrt[3]{\frac{iii}{4 \pi} V}\), where V is the volume of the sphere. Spaceship Earth is a spherical structure at Walt Disney Earth that has an inner radius of about 25 meters. Utilize a graphing figurer to graph the part. Estimate the book of Spaceship World. (Section x.2)
Answer:

Question 17.
The graph of square root function g is shown. Compare the average rate of change of g to the average rate of alter of h(x) = \(\sqrt[3]{\frac{iii}{two} x}\)x over the interval x = 0 to x = 3.

Respond:

Lesson 10.3 Solving Radical Equations

Essential Question How can you solve an equation that contains square roots?

EXPLORATION 1

Analyzing a Free-Falling Object
Work with a partner. The table shows the time t (in seconds) that it takes a complimentary-falling object (with no air resistance) to autumn d feet.

a. Utilize the data in the table to sketch the graph of t as a function of d. Use the coordinate plane below.
b. Use your graph to approximate the time information technology takes the object to fall 240 feet.
c. The relationship between d and t is given by the function t = \(\sqrt{\frac{d}{sixteen}}\).
Employ this function to bank check your estimate in part (b).
d. It takes 5 seconds for the object to hit the ground. How far did it fall? Explain your reasoning.

EXPLORATION 2

Solving a Foursquare Root Equation
Work with a partner. The speed due south (in feet per second) of the free-falling object in Exploration ane is given by the functions
south = \(\sqrt{64d}\).
Discover the distance the object has fallen when it reaches each speed.
a. s = eight ft/sec
b. due south = xvi ft/sec
c. due south = 24 ft/sec

Communicate Your Respond

Question 3.
How can y'all solve an equation that contains foursquare roots?
Respond:

Question iv.
Apply your answer to Question iii to solve each equation.
a. 5 = \(\sqrt{x}\) + xx
b. iv = \(\sqrt{10-eighteen}\)
c. \(\sqrt{x}\) + 2 = three
d. -3 = -2\(\sqrt{x}\)
Answer:

Monitoring Progress

Solve the equation. Bank check your solution.
Question 1.
\(\sqrt{x}\) = half-dozen
Reply:

Question 2.
\(\sqrt{x}\) – 7 = 3
Answer:

Question three.
\(\sqrt{y}\) + xv = 22
Reply:

Question four.
ane – \(\sqrt{c}\) = -2
Reply:

Solve the equation. Check your solution.
Question five.
\(\sqrt{ten+4}\) + 7 = 11
Answer:

Question half dozen.
15 = 6 + \(\sqrt{3w-9}\)
Answer:

Question 7.
\(\sqrt{3x+1}\) = \(\sqrt{4x-vii}\)
Reply:

Question 8.
\(\sqrt{n}\) = \(\sqrt{5n-ane}\)
Answer:

Question 9.
\(\sqrt [3]{ y }\) = 4 = i
Reply:

Question 10.
\(\sqrt [3]{ 3c+7 }\) = 10
Answer:

Solve the equation. Bank check your solution(southward).
Question 11.
\(\sqrt{4-3x}\) = ten
Respond:

Question 12.
\(\sqrt{3m}\) + 10 = one
Respond:

Question 13.
p + 1 = \(\sqrt{7p+15}\)
Answer:

Question 14.
What is the length of a pendulum that has a flow of 2.five seconds?
Answer:

Solving Radical Equations 10.three Exercises

Vocabulary and Core Concept Check

Question 1.
VOCABULARY
Why should you cheque every solution of a radical equation?
Answer:

Question 2.
WHICH One DOESN'T Vest?
Which equation does non belong with the other three? Explain your reasoning.

Answer:

Monitoring Progress and Modeling with Mathematics

In Exercises 3–12, solve the equation. Check your solution.
Question 3.
\(\sqrt{10}\) = nine
Answer:

Question four.
\(\sqrt{x}\) = 4
Answer:

Question v.
7 = \(\sqrt{x}\) – 5
Answer:

Question half-dozen.
\(\sqrt{p}\) – 7 = -1
Answer:

Question 7.
\(\sqrt{c}\) + 12 = 23
Answer:

Question 8.
\(\sqrt{x}\) + 6 = 8
Reply:

Question 9.
four – \(\sqrt{ten}\) = 2
Answer:

Question 10.
-8 = 7 = \(\sqrt{r}\)
Answer:

Question 11.
3\(\sqrt{y}\) – 18 = -3
Reply:

Question 12.
ii\(\sqrt{q}\) + five = eleven
Respond:

In Exercises 13–twenty, solve the equation. Check your solution.
Question xiii.
\(\sqrt{a-3}\) + 5 = 9
Reply:

Question 14.
\(\sqrt{b+7}\) – five = -2
Answer:

Question 15.
two \(\sqrt{ten+4}\) = sixteen
Answer:

Question 16.
5\(\sqrt{y-2}\) = ten
Answer:

Question 17.
-1 = \(\sqrt{5r+ane}\) – vii
Answer:

Question 18.
2 = \(\sqrt{4s-4}\) – iv
Answer:

Question 19.
7 + three\(\sqrt{3p-9}\) = 25
Reply:

Question 20.
19 – 4\(\sqrt{3c-11}\) = 11
Respond:

Question 21.
MODELING WITH MATHEMATICS
The Cave of Swallows is a natural open-air pit cave in the state of San Luis Potosí, Mexico. The 1220-pes- deep cave was a popular destination for BASE jumpers. The function t = \(\frac{1}{four} \sqrt{d}\) represents the time t (in seconds) that it takes a BASE jumper to autumn d anxiety. How far does a BASE jumper fall in 3 seconds?

Respond:

Question 22.
MODELING WITH MATHEMATICS
The border length s of a cube with a surface area of A is given by south = \(\sqrt{\frac{A}{vi}}\). What is the surface surface area of a cube with an edge length of iv inches?

Answer:

In Exercises 23–26, employ the graph to solve the equation.
Question 23.

Reply:

Question 24.

Reply:

Question 25.

Answer:

Question 26.

Reply:

In Exercises 27–34, solve the equation. Check your solution. (See Example 3.)
Question 27.
\(\sqrt{2x-9}\) = \(\sqrt{x}\)
Reply:

Question 28.
\(\sqrt{y+ane}\) = \(\sqrt{4y-eight}\)
Answer:

Question 29.
\(\sqrt{3g+i}\) = \(\sqrt{7g-19}\)
Respond:

Question 30.
\(\sqrt{8h-seven}\) = \(\sqrt{6h+7}\)
Answer:

Question 31.
\(\sqrt{\frac{p}{2}-2}\) = \(\sqrt{p-8}\)
Reply:

Question 32.
\(\sqrt{2v-five}\) = \(\sqrt{\frac{5}{3}+5}\)
Answer:

Question 33.
\(\sqrt{2c+1}\) = \(\sqrt{4c}\) = 0
Reply:

Question 34.
\(\sqrt{5r}\) – \(\sqrt{8r-2}\) = 0
Respond:

MATHEMATICAL CONNECTIONS In Exercises 35 and 36, find the value of 10.
Question 35.
Perimeter = 22 cm

Answer:

Question 36.

Reply:

In Exercises 37–44, solve the equation. Bank check your solution.
Question 37.
\(\sqrt [3]{ x }\) = 4
Answer:

Question 38.
\(\sqrt [iii]{ y }\) = 2
Answer:

Question 39.
6 = 3\(\sqrt [iii]{ 8g }\)
Answer:

Question xl.
\(\sqrt [iii]{ r+19 }\) = 3
Answer:

Question 41.
\(\sqrt [3]{ 2x+nine }\) = -three
Answer:

Question 42.
-v = \(\sqrt [3]{ 10x+15 }\)
Answer:

Question 43.
\(\sqrt [three]{ y+vi }\) = \(\sqrt [3]{ 5y-2 }\)
Answer:

Question 44.
\(\sqrt [3]{ 7j-2 }\) = \(\sqrt [iii]{ j+4 }\)
Answer:

In Exercises 45–48, determine which solution, if whatever, is an extraneous solution.
Question 45.
\(\sqrt{6x-5}\) = x; x = 5, ten = 1
Answer:

Question 46.
\(\sqrt{2y+iii}\) = y; y = -i, y = three
Reply:

Question 47.
\(\sqrt{12p+16}\) = -2p; p = -i, p = 4
Answer:

Question 48.
-3g = \(\sqrt{-18-27}\); chiliad = -2, 1000 = -ane
Reply:

In Exercises 49–58, solve the equation. Check your solution(southward).
Question 49.
y = \(\sqrt{5y-4}\)
Answer:

Question l.
\(\sqrt{-14x-9x}\) = ten
Answer:

Question 51.
\(\sqrt{ane-3a}\) = 2a
Answer:

Question 52.
2q = \(\sqrt{10q-6}\)
Answer:

Question 53.
9 + \(\sqrt{5p}\) = 4
Answer:

Question 54.
\(\sqrt{3n}\) – 11 = -5
Respond:

Question 55.
\(\sqrt{2m+ii}\) – three = 1
Answer:

Question 56.
15 + \(\sqrt{4b-eight}\) = 13
Answer:

Question 57.
r + iv = \(\sqrt{-4r-xix}\)
Answer:

Question 58.
\(\sqrt{3-south}\) = s – 1
Answer:

Fault ANALYSIS In Exercises 59 and 60, describe and correct the error in solving the equation.
Question 59.

Reply:

Question 60.

Answer:

Question 61.
REASONING
Explain how to apply mental math to solve \(\sqrt{2x}\) + 5 = 1.
Respond:

Question 62.
WRITING
Explicate how you would solve \(\sqrt [4]{ chiliad+4 }\) – \(\sqrt [4]{ 3m }\) = 0.
Reply:

Question 63.
MODELING WITH MATHEMATICS
The formula 5 = \(\sqrt{PR}\) relates the voltage Five (in volts), power P (in watts), and resistance R (in ohms) of an electrical circuit. The hair dryer shown is on a 120-volt circuit. Is the resistance of the hair dryer half equally much as the resistance of the aforementioned hair dryer on a 240-volt circuit? Explain your reasoning.

Answer:

Question 64.
MODELING WITH MATHEMATICS
The time t (in seconds) information technology takes a trapeze creative person to swing back and along is represented by the function t = 2π \(\sqrt{\frac{r}{32}}\), where r is the rope length (in feet). It takes the trapeze artist half dozen seconds to swing back and forth. Is this rope \(\frac{3}{two}\) as long every bit the rope used when it takes the trapeze artist four seconds to swing back and along? Explain your reasoning.

Answer:

REASONING In Exercises 65–68, decide whether the statement is true or fake. If it is false, explain why.
Question 65.
If \(\sqrt{a}\) = b, and then (\(\sqrt{a}\))² = b^two.
Respond:

Question 66.
If \(\sqrt{a}\) = \(\sqrt{b}\), and so a = b.
Answer:

Question 67.
If a² = b², then a = b.
Answer:

Question 68.
If a² = \(\sqrt{b}\), then a⁴ = (\(\sqrt{b}\))ⁱⁱ
Answer:

Question 69.
Comparing METHODS
Consider the equation x + 2 = \(\sqrt{2x-3}\).
a. Solve the equation past graphing. Draw the process.
b. Solve the equation algebraically. Draw the process.
c. Which method practice you prefer? Explain your reasoning.
Reply:

Question lxx.
HOW DO You lot Run into It?
The graph shows two radical functions.

a. Write an equation whose solution is the x-coordinate of the betoken of intersection of the graphs.
b. Utilise the graph to solve the equation.
Answer:

Question 71.
MATHEMATICAL CONNECTIONS
The slant elevation s of a cone with a radius of r and a height of h is given past south = \(\sqrt{r^{2}+h^{2}}\). The camber heights of the two cones are equal. Find the radius of each cone.

Reply:

Question 72.
CRITICAL THINKING
How is squaring \(\sqrt{ten+2}\) different from squaring \(\sqrt{x}\) + 2?
Answer:

USING Construction In Exercises 73–78, solve the equation. Check your solution.
Question 73.
\(\sqrt{chiliad+15}\) = \(\sqrt{grand}\) + \(\sqrt{5}\)
Answer:

Question 74.
2 = \(\sqrt{10+1}\) = \(\sqrt{10+2}\)
Answer:

Question 75.
\(\sqrt{5y+ix}\) + \(\sqrt{5y}\) = ix
Reply:

Question 76.
\(\sqrt{2c-8}\) – \(\sqrt{2c}\) – 4 = 0
Respond:

Question 77.
two\(\sqrt{1+4h}\) – 4\(\sqrt{h}\) – 2 = 0
Respond:

Question 78.
\(\sqrt{20-4z}\) + 2\(\sqrt{-z}\) = 10
Answer:

Question 79.
Open-ENDED
Write a radical equation that has a solution of 10 = 5.
Answer:

Question eighty.
OPEN-Ended
Write a radical equation that has 10 = 3 and ten = four as solutions.
Answer:

Question 81.
MAKING AN ARGUMENT
Your friend says the equation \(\sqrt{(2 x+5)^{2}}\) = 2x + 5 is always true, considering after simplifying the left side of the equation, the outcome is an equation with infinitely many solutions. Is your friend correct? Explicate.
Answer:

Question 82.
Idea PROVOKING
Solve the equation \(\sqrt [iii]{ 10+ane }\) = \(\sqrt{x-3}\). Show your work and explain your steps.
Answer:

Question 83.
MODELING WITH MATHEMATICS
The frequency f (in cycles per second) of a string of an electrical guitar is given by the equation f = \(\frac{1}{2 \ell} \sqrt{\frac{T}{m}}\), where ℓ is the length of the string (in meters), T is the string's tension (in newtons), and k is the cord'south mass per unit of measurement length (in kilograms per meter). The high East string of an electric guitar is 0.64 meter long with a mass per unit length of 0.000401 kilogram per meter.

a. How much tension is required to produce a frequency of about 330 cycles per 2nd?
b. Would y'all need more than or less tension to create the aforementioned frequency on a string with greater mass per unit of measurement length? Explain.
Answer:

Maintaining Mathematical Proficiency

Find the product.(Section 7.2)
Question 84.
(x + 8)(x – 2)
Answer:

Question 85.
(3p – 1)(4p + v)
Answer:

Question 86.
(s + 2)(sⁱⁱ + 3s – four)
Reply:

Graph the function. Compare the graph to the graph of f(x) = x².(Department 8.1)
Question 87.
r(x) = 3x²
Answer:

Question 88.
yard(x) = \(\frac{3}{four}\)x²
Answer:

Question 89.
h(x) = -5x²
Answer:

Lesson 10.4 Changed of a Function

Essential Question How are a function and its changed related?

EXPLORATION ane

Exploring Inverse Functions
Work with a partner. The functions f and g are inverses of each other. Compare the tables of values of the two functions. How are the functions related?

EXPLORATION 2

Exploring Inverse Functions
Piece of work with a partner.
a. Plot the 2 sets of points represented by the tables in Exploration i. Use the coordinate plane below.
b. Connect each set of points with a smooth bend.
c. Describe the relationship betwixt the two graphs.
d. Write an equation for each role.

Communicate Your Answer

Question 3.
How are a office and its inverse related?
Reply:

Question 4.
A table of values for a office f is given. Create a tabular array of values for a office g, the inverse of f.

Reply:

Question 5.
Sketch the graphs of f(x) = x + 4 and its inverse in the same coordinate plane. Then write an equation of the changed of f. Explain your reasoning.

Answer:

Monitoring Progress

Detect the changed of the relation.
Question 1.
(-iii, -4), (-2, 0), (-1, 4), (0, 8), (1, 12), (2, 16), (3, 20)
Respond:

Question 2.

Answer:

Solve y = f(ten) for x. Then find the input when the output is 4.
Question 3.
f(x) = x – 6
Answer:

Question 4.
f(x) = \(\frac{ane}{2}\)10 + 3
Answer:

Question five.
f(ten) = 4x²
Answer:

Observe the inverse of the function. Then graph the part and its inverse.
Question 6.
f(x) = 6x
Respond:

Question 7.
f(x) = -ten + v
Answer:

Question viii.
f(x) = \(\frac{1}{4}\)10 – 1
Reply:

Find the inverse of the office. And then graph the role and its inverse.
Question nine.
f(x) = -x^two, x ≤ 0
Answer:

Question 10.
f(x) = 4xⁱⁱ + 3, ten ≥ 0
Answer:

Question 11.
Is the inverse of f(x) = \(\sqrt{2x-1}\) a function? Find the changed.
Answer:

Inverse of a Function 10.iv Exercises

Vocabulary and Core ConceptCheck

Question ane.
COMPLETE THE Judgement
A relation contains the point (-iii, 10). The ____________ contains the point (10, -three).
Reply:

Question 2.
DIFFERENT WORDS, SAME QUESTION
Consider the function f represented by the graph. Which is different? Detect "both" answers.

Reply:

In Exercises 3–8, observe the changed of the relation.
Question 3.
(1, 0), (3, -viii), (4, -3), (7, -5), (9, -1)
Answer:

Question 4.
(2, ane), (iv, -iii), (6, seven), (8, 1), (ten, -4)
Answer:

Question 5.

Answer:

Question 6.

Answer:

Question seven.

Reply:

Question eight.

Answer:

In Exercises nine–14, solve y = f(x) for x. And then find the input when the output is 2.
Question nine.
f(x) = x + five
Answer:

Question 10.
f(10) = 2x – three
Reply:

Question xi.
f(x) = \(\frac{i}{four}\)x – 1
Respond:

Question 12.
f(x) = \(\frac{two}{3}\)x + four
Reply:

Question 13.
f(x) = 9x²
Reply:

Question xiv.
f(x) = \(\frac{1}{two}\)xⁱⁱ – 7
Answer:

In Exercises 15 and xvi, graph the changed of the function by reflecting the graph in the line y = x. Describe the domain and range of the inverse.
Question 15.

Respond:

Question sixteen.

Answer:

In Exercises 17–22, discover the inverse of the part. Then graph the office and its inverse.
Question 17.
f(10) = 4x – one
Respond:

Question 18.
f(10) = -2x + v
Respond:

Question 19.
f(x) = -3x – 2
Answer:

Question 20.
f(x) = 2x + 3
Reply:

Question 21.
f(x) =\(\frac{one}{3}\)ten + 8
Answer:

Question 22.
f(x) = – \(\frac{three}{two}\)x + \(\frac{7}{2}\)
Answer:

In Exercises 23–28, find the inverse of the function. So graph the part and its inverse.
Question 23.
f(10) = 4x^two, 10 ≥ 0
Answer:

Question 24.
f(x) = \(\frac{2}{25}\)10ⁱⁱ, 10 ≤ 0
Answer:

Question 25.
f(x) = -ten² + 10, x ≤ 0
Answer:

Question 26.
f(x) = 2x² + six, x ≥ 0
Answer:

Question 27.
f(x) = \(\frac{ane}{9}\)x² + 2, 10 ≥ 0
Answer:

Question 28.
f(ten) = -4xⁱⁱ – viii, x ≤ 0
Answer:

In Exercises 29–32, use the Horizontal Line Test to make up one's mind whether the inverse of f is a function.
Question 29.

Answer:

Question 30.

Respond:

Question 31.

Answer:

Question 32.

Answer:

In Exercises 33–42, determine whether the inverse of f is a office. Then detect the inverse.
Question 33.
f(ten) = \(\sqrt{x+3}\)
Answer:

Question 34.
f(10) = \(\sqrt{x-5}\)
Respond:

Question 35.
f(x) = \(\sqrt{2x-6}\)
Respond:

Question 36.
f(ten) = \(\sqrt{4x+1}\)
Answer:

Question 37.
f(x) = 3\(\sqrt{10-8}\)
Reply:

Question 38.
f(ten) = –\(\frac{i}{4} \sqrt{5 x+2}\)
Answer:

Question 39.
f(x) = –\(\sqrt{3x+5}\) – two
Respond:

Question twoscore.
f(x) = ii\(\sqrt{10-7}\) + 6
Answer:

Question 41.
f(x) = 2x²
Answer:

Question 42.
f(x) = |x|
Answer:

Question 43.
Fault ANALYSIS
Describe and right the fault in finding the changed of the function f(x) = – 3x + 5.

Answer:

Question 44.
Mistake Analysis
Describe and right the error in finding and graphing the inverse of the function f(10) = \(\sqrt{10-3}\).

Answer:

Question 45.
MODELING WITH MATHEMATICS
The euro is the unit of currency for the European Matrimony. On a certain day, the number E of euros that could be obtained for D U.S. dollars was represented past the formula shown.
E = 0.74683D
Solve the formula for D. Then find the number of U.S. dollars that could exist obtained for 250 euros on that twenty-four hours.
Answer:

Question 46.
MODELING WITH MATHEMATICS
A crow is flying at a height of 50 feet when information technology drops a walnut to intermission information technology open up. The height h (in anxiety) of the walnut to a higher place ground can be modeled past h = -16t² + 50, where t is the fourth dimension (in seconds) since the crow dropped the walnut. Solve the equation for t. Afterward how many seconds will the walnut exist 15 feet higher up the footing?

Answer:

MATHEMATICAL CONNECTIONS In Exercises 47 and 48, s is the side length of an equilateral triangle. Solve the formula for due south. Then evaluate the new formula for the given value.

Reply:
47.

In Exercises 49–54, detect the inverse of the part. Then graph the function and its inverse.
Question 49.
f(ten) = 2x³
Respond:

Question 50.
f(x) = xⁱⁱⁱ – 4
Answer:

Question 51.
f(x) = (ten – 5)³
Answer:

Question 52.
f(x) = 8(x + 2)^three
Answer:

Question 53.
f(10) = 4\(\sqrt [3]{ x }\)
Answer:

Question 54.
f(10) = –\(\sqrt [iii]{ 10-1 }\)
Reply:

Question 55.
MAKING AN ARGUMENT
Your friend says that the inverse of the function f(ten) = 3 is a function because all linear functions pass the Horizontal Line Test. Is your friend correct? Explain.
Answer:

Question 56.
HOW DO YOU SEE It?
Pair the graph of each role with the graph of its inverse.

Answer:

Question 57.
WRITING
Describe changes you could make to the function f(ten) = x^two – five and so that its inverse is a office. Describe the domain and range of the new function and its changed.
Answer:

Question 58.
CRITICAL THINKING
Tin can an even function with at least two values in its domain have an changed that is a office? Explicate.
Respond:

Question 59.
OPEN-ENDED
Write a function such that the graph of its inverse is a line with a gradient of 4.
Reply:

Question 60.
CRITICAL THINKING
Consider the function g(10) = -x.
a. Graph g(10) = -x and explain why it is its own inverse.
b. Graph other linear functions that are their own inverses. Write equations of the lines yous graph.
c. Use your results from part (b) to write a general equation that describes the family of linear functions that are their own inverses.
Answer:

Question 61.
REASONING
Testify that the inverse of whatsoever linear function f(x) = mx + b, where 1000 ≠ 0, is also a linear function. Write the slope and y-intercept of the graph of the inverse in terms of m and b.
Respond:

Question 62.
THOUGHT PROVOKING
The graphs of f(x) = 10³ – 3x and its inverse are shown. Find the greatest interval -a ≤ x ≤ a for which the inverse of f is a part. Write an equation of the inverse office.

Answer:

Question 63.
REASONING
Is the changed of f(x) = two|x + i|a function? Are there any values of a, h, and m for which the inverse of f(x) = a |x – h| + k is a function? Explain your reasoning.
Answer:

Maintaining Mathematical Proficiency

Notice the sum or difference.(Section 7.one)
Question 64.
(2x – ix) – (6x + 5)
Respond:

Question 65.
(8y + 1) + (-y – 12)
Answer:

Question 66.
(t² – 4t – iv) + (7t² + 12t + 3)
Answer:

Question 67.
(-3dⁱⁱ + 10d – 8) – (7d² – d – 6)
Respond:

Graph the function. Compare the graph to the graph of f(10) = x². (Section 8.2)
Question 68.
g(x) = x^two + vi
Respond:

Question 69.
h(x) = -ten² – 2
Reply:

Question 70.
p(x) = -4x^two + 5
Reply:

Question 71.
q(x) = \(\frac{1}{3}\)ten^two – ane
Answer:

Radical Functions and Equations Functioning Task: Medication and the Mosteller Formula

10.3–x.4What Did YouLearn?

Cadre Vocabulary
radical equation, p. 560
inverse relation, p. 568
changed role, p. 569

Core Concepts
Lesson 10.three
Squaring Each Side of an Equation, p. 560
Identifying Inapplicable Solutions, p. 562

Lesson x.4
Inverse Relation, p. 568
Finding Inverses of Functions Algebraically, p. 570
Finding Inverses of Nonlinear Functions, p. 570
Horizontal Line Exam, p. 571

Mathematical Practices
Question 1.
Could you also solve Exercises 37–44 on page 565 past graphing? Explain.
Answer:

Question 2.
What external resources could you utilise to bank check the reasonableness of your answer in Exercise 45 on page 573?
Answer:

Performance Task: Medication and the Mosteller Formula

When taking medication, it is critical to take the correct dosage. For children in item, body surface area (BSA) is a key component in computing that dosage. The Mosteller Formula is commonly used to approximate body surface area. How will you use this formula to calculate BSA for the optimum dosage?
To explore the answers to this question and more, get to

Radical Functions and Equations Chapter Review

10.i Graphing Square Root Functions (pp. 543–550)

Graph the office. Describe the domain and range. Compare the graph to the graph of f(x) = \(\sqrt{x}\).
Question ane.
one thousand(x) = \(\sqrt{x}\) + 7
Answer:

Question ii.
h(x) = \(\sqrt{ten-half-dozen}\)
Answer:

Question 3.
r(x) = –\(\sqrt{x+iii}\) – 1
Answer:

Question four.
Permit k(x) = \(\frac{1}{4} \sqrt{x-6}\) + 2. Describe the transformations from the graph of f(x) = \(\sqrt{10}\) to the graph of g. Then graph g.
Reply:

10.two Graphing Cube Root Functions (pp. 551–556)

Graph the function. Compare the graph to the graph of f(x) = \(\sqrt [3]{ x }\).
Question 5.
g(x) = \(\sqrt [3]{ x }\) + iv
Answer:

Question 6.
h(x) = -8\(\sqrt [three]{ 10 }\)
Answer:

Question 7.
s(x) = \(\sqrt[3]{-2(x-three)}\)
Answer:

Question 8.
Permit thousand(x) = -3\(\sqrt [3]{ ten+two }\) – 1. Describe the transformations from the graph of f(10) = \(\sqrt [three]{ ten }\) to the graph of 1000. Then graph g.
Answer:

Question 9.
The graph of cube root office r is shown. Compare the average rate of change of r to the average rate of change of p(x) = \(\sqrt[three]{\frac{1}{2} 10}\) over the interval x = 0 to ten = 8.
Respond:

x.iii Solving Radical Equations (pp. 559-566)

Solve the equation. Check your solution(s).
Question 10.
8 + \(\sqrt{x}\) = eighteen
Reply:

Question eleven.
\(\sqrt [3]{ x-1 }\) = three
Answer:

Question 12.
\(\sqrt{5x-ix}\) = \(\sqrt{4x}\)
Respond:

Question 13.
x = \(\sqrt{3x+four}\)
Answer:

Question 14.
viii\(\sqrt{10-5}\) + 34 = 58
Reply:

Question 15.
\(\sqrt{5x}\) + half-dozen = 5
Answer:

Question 16.
The radius r of a cylinder is represented by the function r = \(\sqrt{\frac{Five}{\pi h}}\), where V is the volume and h is the height of the cylinder. What is the volume of the cylindrical tin can?

Answer:

10.4 Inverse of a Office (pp. 567–574)

Find the inverse of the relation.
Question 17.
(1, -10), (3, -4), (five, iv), (7, 14), (9, 26)
Answer:

Question 18.

Respond:

Discover the changed of the office. Then graph the function and its changed.
Question xix.
f(x) = -5x + 10
Respond:

Question 20.
f(x) = 3x² – 1, ten ≥ 0
Answer:

Question 21.
f(ten) = \(\frac{i}{two} \sqrt{ii x+6}\)
Respond:

Question 22.
Consider the function f(ten) = x² + 4. Use the Horizontal Line Test to make up one's mind whether the inverse of f is a function.
Answer:

Question 23.
In bowling, a handicap is an aligning to a bowler'southward score to even out differences in ability levels. In a particular league, you lot can detect a bowler's handicap h past using the formula h = 0.8(210 – a), where a is the bowler's average. Solve the formula for a. And so find a bowler'southward boilerplate when the bowler's handicap is 28.

Answer:

Radical Functions and Equations Chapter Test

Find the inverse of the office.
Question one.
f(x) = 5x – 8 2.
Answer:

Question 2.
f(10) = 2\(\sqrt{10+3}\) – 1
Respond:

Question iii.
f(x) = –\(\frac{1}{3}\)xⁱⁱ + iv, 10 ≥ 0
Answer:

Graph the role f. Describe the domain and range. Compare the graph of f to the graph of thou.
Question iv.
f(x) = –\(\sqrt{x+6}\); g(x) = \(\sqrt{x}\)
Answer:

Question 5.
f(x) = \(\sqrt{x-three}\) + 2; 1000(x) = \(\sqrt{x}\)
Answer:

Question 6.
f(x) = \(\sqrt [3]{ x }\) – five; m(10) = \(\sqrt [3]{ x }\)
Reply:

Question 7.
f(x) = -2\(\sqrt [3]{ x+ane }\); g(x) = \(\sqrt [3]{ x }\)
Answer:

Solve the equation. Check your solution(s).
Question 8.
9 – \(\sqrt{x}\) = 3
Answer:

Question ix.
\(\sqrt{2x-7}\) – iii = half dozen
Answer:

Question 10.
\(\sqrt{8x-21}\) = \(\sqrt{eighteen-5x}\)
Answer:

Question eleven.
x + 5 = \(\sqrt{7x+53}\)
Respond:

Question 12.
When solving the equation x – 5 = \(\sqrt{ax+b}\), you lot obtain x = 2 and x = 8. Explain why at to the lowest degree one of these solutions must be inapplicable.
Answer:

Draw the transformations from the graph of f(10) = \(\sqrt [3]{ x }\) to the graph of the given office. Then graph the given part.
Question 13.
h(x) = four\(\sqrt [iii]{ x-1 }\) + 5
Answer:

Question fourteen.
west(x) = –\(\sqrt [three]{ x+7 }\) – ii
Reply:

Question xv.
The velocity v (in meters per second) of a roller coaster at the bottom of a hill is given by v = \(\sqrt{19.6h}\), where h is the height (in meters) of the hill. (a) Employ a graphing calculator to graph the function. Describe the domain and range. (b) How tall must the hill be for the velocity of the roller coaster at the lesser of the hill to exist at least 28 meters per second? (c) What happens to the average rate of change of the velocity as the height of the colina increases?
Reply:

Question 16.
The speed southward (in meters per second) of sound through air is given by s = two\(\sqrt{T+273}\), where T is the temperature (in degrees Celsius).

a. What is the temperature when the speed of sound through air is 340 meters per second?
b. How long does it take you to hear the wolf howl when the temperature is -17°C?
Answer:

Question 17.
How tin can you restrict the domain of the office f(x) = (10 – 3)ⁱⁱ then that the inverse of f is a function?
Answer:

Question eighteen.
Write a radical function that has a domain of all real numbers less than or equal to 0 and a range of all real numbers greater than or equal to 9.
Answer:

Radical Functions and Equations Cumulative Assessment

Question 1.
Make full in the function so that it is represented by the graph.

Answer:

Question two.
Consider the equation y = mx + b. Fill in values for one thousand and b and so that each statement is true.
a. When chiliad = ______ and b = ______, the graph of the equation passes through the point (-1, 4).
b. When thousand = ______ and b = ______, the graph of the equation has a positive slope and passes through the point (-2, -5).
c. When m = ______ and b = ______, the graph of the equation is perpendicular to the graph of y = 4x – 3 and passes through the point (one, 6).
Answer:

Question iii.
Which graph represents the inverse of the function f(x) = 2x + four?

Answer:

Question 4.
Consider the equation x = \(\sqrt{ax+b}\). Student A claims this equation has 1 real solution. Educatee B claims this equation has ii real solutions. Employ the numbers to answer parts (a)–(c).

a. Choose values for a and b to create an equation that supports Student A'south claim.
b. Choose values for a and b to create an equation that supports Student B's claim.
c. Choose values for a and b to create an equation that does not support either student's claim.
Answer:

Question 5.
Which equation represents the nth term of the sequence 3, 12, 48, 192, . . .?
A. a_n = iii(iv)^n-i
B. a_{due north} = 3(9)^northward-1
C. a_{due north} = 9n – vi
D. a_n = 9n + three
Answer:

Question 6.
Consider the function f(x) = \(\frac{1}{2} \sqrt[three]{ten+3}\). The graph represents function thousand. Select all the statements that are truthful.

Reply:

Question vii.
Place each part into one of the iii categories.

Answer:

Question viii.
You are making a tabletop with a tiled center and a uniform mosaic border.
a. Write the polynomial in standard form that represents the perimeter of the tabletop.
b. Write the polynomial in standard form that represents the expanse of the tabletop.
c. The perimeter of the tabletop is less than 80 inches, and the area of tabletop is at least 252 square inches. Select all the possible values of x.

Respond:

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