1.1 practice b - edl · pdf filein exercises 1 and 2, identify the function family to which f...

Copyright © Big Ideas Learning, LLC Algebra 2 All rights reserved. Resources by Chapter

5

1.1 Practice A

Name _________________________________________________________ Date __________

In Exercises 1 and 2, identify the function family to which f belongs. Compare the graph of f to the graph of its parent function.

1. 2.

3. You purchased a computer for your business for $800. Using straight-line depreciation, the amount of depreciation allowed for each year after the purchase is given by the function ( ) 800 114.29 .f x x= − What type of function can you use to model the data?

In Exercises 4–9, graph the function and its parent function. Then describe the transformation.

4. ( ) 2h x x= + 5. ( ) 3f x x= − 6. ( ) 2 2g x x= +

7. ( ) ( )21f x x= − 8. ( ) 4h x x= + 9. ( ) 5f x =


10. ( ) 3f x x= 11. ( ) 12g x x= 12. ( ) 23h x x=

13. ( ) 214g x x= 14. ( ) 2h x x= 15. ( ) 5

2f x x=

In Exercises 16–18, use a graphing calculator to graph the function and its parent function. Then describe the transformations.

16. ( ) 13 1f x x= − 17. ( ) 2 3h x x= − 18. ( ) 25

3 2g x x= +

19. In the same coordinate plane, sketch the graph of a parent absolute-value function and the graph of an absolute-value function that has no x-intercepts. Describe the transformation(s) of the parent function.

x

y

2

−2

2−2

13f(x) = x2 − 1

x

y

1

−2

2−2

f(x) = 2

Algebra 2 Copyright © Big Ideas Learning, LLC Resources by Chapter All rights reserved. 6

1.1 Practice B

Name _________________________________________________________ Date _________

In Exercises 1 and 2, identify the function family to which f belongs. Compare the graph of f with the graph of its parent function.

1. 2.


3. ( ) 2h x x= + 4. ( )f x x= − 5. ( ) 2g x x= −

6. ( ) ( )22f x x= + 7. ( ) 2h x x= − 8. ( ) 3f x = −


9. ( ) 35f x x= 10. ( ) 3

2h x x= 11. ( ) 243h x x=

In Exercises 12–14, use a graphing calculator to graph the function and its parent function. Then describe the transformations.

12. ( ) 2110 5g x x= + 13. ( ) ( )2 4

95h x x= − + 14. ( ) 132f x x= − + −

In Exercises 15–18, identify the function family and describe the domain and range. Use a graphing calculator to verify your answer.

15. ( ) 5 3h x x= + + 16. ( ) 2 10g x x= − − 17. ( ) 27 3g x x= −

18. You are throwing a football with your friends. The height (in feet) of the ball above the ground t seconds after it is thrown is modeled by the function

( ) 216 45 6.f t t t= − + +

a. Without graphing, identify the type of function modeled by the equation.

b. What is the value of t when the ball is released from your hand? Explain.

c. How many feet above the ground is the ball when it is released from your hand? Explain.

x

y

2

−2

2 4

f(x) = #x − 3 #25

x

y

2

−2

2−2

f(x) = 2x + 1

Answers

Copyright © Big Ideas Learning, LLC Algebra 2 All rights reserved. Answers

A1

Chapter 1 1.1 Start Thinking

As the string V gets wider, the points on the string move closer to the x-axis. This activity mimics a vertical shrink of a parabola.

1.1 Warm Up

1. 2.

3. 4.

1.1 Cumulative Review Warm Up

1. 12− 2. 1 3. 1

2 4. 25

1.1 Practice A

1. quadratic; The graph of f is a vertical shrink by a factor of 1

3 followed by a translation 1 unit down

of the graph of the parent quadratic function.

2. constant; The graph of f is a translation 1 unit up of the graph of the parent constant function.

3. a linear function

4.

Sample answer: The graph of h is a translation 2 units up of the graph of the parent linear function.

5.

Sample answer: The graph of f is a translation 3 units right of the parent linear function.

6.

The graph of g is a translation 2 units up of the parent quadratic function.

7.

The graph of f is a translation 1 unit right of the graph of the parent quadratic function.

8.

The graph of h is a translation 4 units left of the graph of the parent function.

9.

The graph of f is a translation 4 units up of the graph of the parent constant function.

−4 −2 2 4 x

y

−4

2

4

−4 −2 2 x

y

2

4

6

−4 −2 2 4 x

y

−4

−2

2

4

−4 −2 2 4 x

y

−6

−2

−4 2 4 x

y

−4

−2

4

h(x) = x + 2

f(x) = x

−4 2 4 x

y

−2

4

f(x) = x − 3

f(x) = x

−4 −2 2 4 x

y

4

6

f(x) = x2g(x) = x2 + 2

−2 2 4 x

y

4

6

f(x) = (x − 1)2f(x) = x2

−4 −2 2 4 x

y

−2

4

2

6

f(x) = 5f(x) = 1

−4−6 −2 2 x

y

2

6

h(x) = $x + 4 $

f(x) = $x $


1.2 Practice A

Name _________________________________________________________ Date _________

In Exercises 1–4, write a function g whose graph represents the indicated transformation of the graph of f. Use a graphing calculator to check your answer.

1. ( ) 2;f x x= − translation 5 units left

2. ( ) 1;f x x= + translation 4 units right

3. ( ) 3 2 4;f x x= + + translation 3 units down

4. ( ) 4 5;f x x= − translation 3 units up


5. ( ) 3 7;f x x= − + reflection in the x-axis

6. ( ) 13 2;f x x= − reflection in the x-axis

7. ( ) 4 6;f x x= − reflection in the y-axis

8. ( ) 3 5 3;f x x= − + reflection in the y-axis


9. ( ) 3;f x x= + vertical stretch by a factor of 4

10. ( ) 4 3;f x x= + vertical shrink by a factor of 13

11. ( ) 3 2;f x x= + horizontal shrink by a factor of 13

12. ( ) 1 ;f x x= + horizontal stretch by a factor of 3

In Exercises 13 and 14, write a function g whose graph represents the indicated transformation of the graph of f.

13. ( ) ;f x x= vertical shrink by a factor of 13 followed by a translation 4 units down

14. ( ) ;f x x= translation 3 units left followed by a horizontal shrink by a factor

of 12


11

1.2 Practice B

Name _________________________________________________________ Date __________


1. ( ) 5 2;f x x= − translation 5 units right

2. ( ) 3 6;f x x= + translation 4 units up

3. ( ) 3 2 ;f x x= − − translation 2 units left

4. ( ) 2 3;f x x= + translation 2 units down


5. ( ) 3;f x x= − + reflection in the y-axis


7. ( ) 5 8 ;f x x= − + − reflection in the y-axis



9. ( ) 3 ;f x x= − horizontal stretch by a factor of 2



12. ( ) 2 2 4;f x x= − − + vertical stretch by a factor of 2


13. ( ) ;f x x= translation 5 units up followed by a vertical shrink by a factor of 14

14. ( ) ;f x x= reflection in the x-axis followed by a translation 2 units left

Answers

Algebra 2 Copyright © Big Ideas Learning, LLC Answers All rights reserved. A2

10.

Sample answer: The graph of f is a vertical stretch by a factor of 3 of the graph of the parent linear function.

11.

Sample answer: The graph of g is a vertical shrink by a factor of 1

2 of the parent linear function.

12.

The graph of h is a vertical stretch by a factor of 3 of the graph of the parent quadratic function.

13.

Sample answer: The graph of g is a vertical shrink by a factor of 1

4 of the graph of the parent quadratic

function.

14.

The graph of h is a vertical stretch by a factor of 2 of the graph of the parent absolute value function.

15.

Sample answer: The graph of f is a vertical stretch by a factor of 5

2 of the graph of the parent linear

function.

16.

The graph of f is a vertical shrink by a factor of 13

followed by a translation 1 unit down of the graph of the parent linear function.

17.

The graph of h is a vertical stretch by a factor of 2 followed by a translation 3 units down of the graph of the parent absolute value function.

−4 −2 2 4 x

y

−4

−2

4

f(x) = x

g(x) = x12

−4 −2 2 4 x

y

4

6

f(x) = x2h(x) = 3x2

−4 −2 2 4 x

y

4

2

6f(x) = x2

g(x) = x214

−4 −2 2 4 x

y

4

2

−2

6

f(x) = #x #h(x) = 2 #x #

−4 −2 2 4 x

y

−4

4

f(x) = x

f(x) = x52

−4 −2 4 x

y

−2

−4

4

2

f(x) = x − 1

f(x) = x

13

−4 −2 2 4 x

y4

2

−4

f(x) = #x #

h(x) = 2 #x # − 3

−4 −2 2 4 x

y

−4

4

2

f(x) = 3x

f(x) = x

Answers

Copyright © Big Ideas Learning, LLC Algebra 2 All rights reserved. Answers

A3

18.

The graph of g is a vertical stretch by a factor of 53

followed by a translation 2 units up of the graph of the parent quadratic function.

19. Sample answer:

The graph of g is a translation 3 units up of the graph of the parent absolute value function.

1.1 Practice B

1. absolute value; The graph of f is a vertical shrink by a factor of 2

5 followed by a translation 3 units right

of the graph of the parent absolute value function.

2. linear; The graph of f is a vertical stretch by a factor of 2 followed by a translation 1 unit up of the graph of the parent linear function.

3.

Sample answer: The graph of h is a translation 2 units up of the graph of the parent linear function.

4.

Sample answer: The graph of f is a reflection in the x-axis of the graph of the parent linear function.

5.

The graph of g is a reflection in the x-axis of the graph of the parent quadratic function.

6.

The graph of f is a translation 2 units left of the graph of the parent quadratic function.

7.

The graph of h is a translation 2 units down of the graph of the parent absolute value function.

8.

The graph of f is a translation 4 units down of the parent constant function.

−4 −2 2 4 x

y

4

6f(x) = x2

g(x) = x2 + 253

−4 −2 2 4 x

y

4

2

6

f(x) = $x $g(x) = $x $ + 3

−4 2 4 x

y

−4

−2

4

h(x) = x + 2

f(x) = x

−4 −2 2 4 x

y

−4

−2

4

2

f(x) = xf(x) = −x

−4 −2 2 4 x

y

−4

−2

4

2

f(x) = x2

g(x) = −x2

−4 −2 2 4 x

y4

2

−4h(x) = $x $ − 2

f(x) = $x $

−4 −2 2 4 x

y

−2

−4

4

2

f(x) = −3

f(x) = 1

−4 −2 2 4 x

y

4

6

f(x) = x2f(x) = (x + 2)2

Answers

Algebra 2 Copyright © Big Ideas Learning, LLC Answers All rights reserved. A4

9.

Sample answer: The graph of f is a vertical shrink by a factor of 3

5 of the graph of the parent linear

function.

10.

Sample answer: The graph of h is a vertical stretch by a factor of 3

2 of the graph of the parent absolute

value function.

11.

The graph of h is a vertical stretch by a factor of 43

of the graph of the parent quadratic function.

12.

The graph of g is a vertical shrink by a factor of 110

followed by a translation 5 units up of the graph of the parent quadratic function.

13.

The graph of h is a translation 5 units right and 49

units up of the graph of the parent quadratic function.

14.

The graph of f is a reflection in the x-axis, followed by a translation 2 units left and 1

3 units down of the

graph of the parent absolute value function.

15. absolute value; domain: all real numbers, range: 3y ≥

16. linear; domain: all real numbers, range: all real numbers

17. quadratic; domain: all real numbers, range: 3y ≥ −

18. a. quadratic function b. 0; t is the number of seconds after the ball is

thrown, so when the ball is thrown 0.t =

c. 6 ft; ( )0 6f =

1.1 Enrichment and Extension

1.

Sample answer: Trapezoid A B C D′ ′ ′ ′ a reflection in the x-axis, followed by translation 1 unit down and 6 units left of trapezoid ABCD.

−4 −2 42 x

y

−2

−4

4

2

f(x) = x35

f(x) = x

−4 −2 2 4 x

y

4

2

6

f(x) = #x #

h(x) = #x #32

−4 −2 2 4 x

y

4

2

6

f(x) = x2

h(x) = x243

−4 −2 2 4 x

y

4

2

6

8

f(x) = x2

g(x) = x2 + 5110

2 4 x

y

4

2

6

f(x) = x2h(x) = (x − 5)2 + 49

−4 2 4 x

y4

2

−4

f(x) = #x #

f(x) = −#x + 2 # − 13

x

y

2

2 6−4−6

A D

CB

A′ D′

C′B′


1.2 Practice A

Name _________________________________________________________ Date _________


1. ( ) 2;f x x= − translation 5 units left

2. ( ) 1;f x x= + translation 4 units right

3. ( ) 3 2 4;f x x= + + translation 3 units down

4. ( ) 4 5;f x x= − translation 3 units up


5. ( ) 3 7;f x x= − + reflection in the x-axis


7. ( ) 4 6;f x x= − reflection in the y-axis



9. ( ) 3;f x x= + vertical stretch by a factor of 4



12. ( ) 1 ;f x x= + horizontal stretch by a factor of 3


13. ( ) ;f x x= vertical shrink by a factor of 13 followed by a translation 4 units down

14. ( ) ;f x x= translation 3 units left followed by a horizontal shrink by a factor

of 12


11

1.2 Practice B

Name _________________________________________________________ Date __________


1. ( ) 5 2;f x x= − translation 5 units right

2. ( ) 3 6;f x x= + translation 4 units up

3. ( ) 3 2 ;f x x= − − translation 2 units left

4. ( ) 2 3;f x x= + translation 2 units down


5. ( ) 3;f x x= − + reflection in the y-axis


7. ( ) 5 8 ;f x x= − + − reflection in the y-axis



9. ( ) 3 ;f x x= − horizontal stretch by a factor of 2



12. ( ) 2 2 4;f x x= − − + vertical stretch by a factor of 2


13. ( ) ;f x x= translation 5 units up followed by a vertical shrink by a factor of 14

14. ( ) ;f x x= reflection in the x-axis followed by a translation 2 units left


15

1.3 Practice A

Name _________________________________________________________ Date __________

In Exercises 1 and 2, use the graph to write an equation of the line and interpret the slope.

1. 2.

3. Two car washes charge a basic fee plus a fee based on the number of extras that are chosen. The table below shows the total costs for different car washes at Bubbles Car Wash. The total cost y (in dollars) for a car wash with x extras at Soapy Car Wash is represented by the equation 9.y x= + Which car wash charges more for the basic fee? How many extras must be chosen for the total costs to be the same?

In Exercises 4 and 5, determine whether the data show a linear relationship. If so, write an equation of a line of fit. Estimate y when x 15= and explain its meaning in the context of the situation.

4.

5.

6. A set of data points has a correlation coefficient 0.86.r = − Your friend claims that because the correlation coefficient is close to 1,− it is reasonable to use the line of best fit to make predictions. Is your friend correct? Explain your reasoning.

00

4

8

50 100

Sale

s ta

x (d

olla

rs)

150 200 250 x

y

Cost of room (dollars)

12

Hotel Stay

(200, 12)

3

50

00

4

8

2 4

Soap

(oun

ces)

6 8 10 x

y

Time (days)

12

Soap in Bottle

24

Number of extras, x 2 4 6 8

Total cost, y 9 12 15 18

Weeks, x 3 6 10 12 16

Height of basil plant (inches), y 1 2 5 9 15

Minutes, x 6 10 14 20 24

Cars washed, y 3 5 7 10 12


1.3 Practice B

Name _________________________________________________________ Date _________

In Exercises 1 and 2, use the graph to write an equation of the line and interpret the slope.

1. 2.

In Exercises 3 and 4, determine whether the data show a linear relationship. If so, write an equation of a line of fit. Estimate y when x 15= and explain its meaning in the context of the situation.

3.

4.

In Exercises 5 and 6, use the linear regression feature on a graphing calculator to find an equation of the line of best fit for the data. Find and interpret the correlation coefficient.

5. 6.

00

20

40

2 4

Wei

ght

(pou

nds)

6 x

y

Age (years)

Child’s Weight

(5, 40)10

2

00

8

16

2 4

Brea

d (lo

aves

)

6 x

y

Flour (cups)

Flour Remaining

(0, 20)

(4, 9)4

11

Days, x 3 7 11 14 20

Number of tickets sold, y 76 164 252 318 450

Minutes running, x 6 10 17 25 40

Calories burned, y 70 118 200 295 472

00

2

4

2 4 6 x

y

00

2

4

2 4 6 x

y

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Period____Date________________Absolute Value InequalitiesSolve each inequality and graph its solution.

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Period____Date________________Solving Absolute Value Equations

Solve each equation.

1)

3

x = 9 2)

−3

r = 9

3)

b

5 = 1

4)

−6

m = 30

5)

n

3 = 2

6)

−4 + 5

x = 16

7)

−2

r − 1 = 11 8)

1 − 5

a = 29

9)

−2

n + 6 = 6 10)

v + 8 − 5 = 2

-1-

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11)

5

x + 5 = 45 12)

3 −8

x + 8 = 80

13)

5 −

8 −2

n = −75 14)

−5

3 + 4

k = −115

15)

7

p + 4

8 = 3

16)

3 −

8

x − 6 = 3

17)

2 −

5

5

m − 5 = −73 18)

6

1 − 5

x − 9 = 57

19)

3

3 − 5

r − 3 = 18 20)

5

9 − 5

n − 7 = 38

-2-

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Period____Date________________Solving Absolute Value Equations

Solve each equation.

1)

3

x = 9

{3, −3}

2)

−3

r = 9

{−3, 3}

3)

b

5 = 1

{5, −5}

4)

−6

m = 30

{−5, 5}

5)

n

3 = 2

{6, −6}

6)

−4 + 5

x = 16

{4,

−12

5 }

7)

−2

r − 1 = 11

{−6, 5}

8)

1 − 5

a = 29

{

−28

5, 6}

9)

−2

n + 6 = 6

{0, 6}

10)

v + 8 − 5 = 2

{−1, −15}

-1-

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11)

5

x + 5 = 45

{8, −8}

12)

3 −8

x + 8 = 80

{−3, 3}

13)

5 −

8 −2

n = −75

{−5, 5}

14)

−5

3 + 4

k = −115

{5,

−13

2 }

15)

7

p + 4

8 = 3

{

20

7, −4}

16)

3 −

8

x − 6 = 3

{

3

4}

17)

2 −

5

5

m − 5 = −73

{4, −2}

18)

6

1 − 5

x − 9 = 57

{−2,

12

5 }

19)

3

3 − 5

r − 3 = 18

{

−4

5, 2}

20)

5

9 − 5

n − 7 = 38

{0,

18

5 }

-2-

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