Functions3D

ex plo rat i o n

Copyright © by Holt, Rinehart and Winston. 81 Holt MathematicsAll rights reserved.

A function is a rule that assigns one output value for each inputvalue. An input/output table is a convenient way of representingfunctions.

1. Complete the table by applying the rule to each input value.

Rule:Input x 2000 � 25x Output y

0 2000 � 25(0) � 2000 2000

1

2

3

Input x Rule Output y

2 0

4 2

6 4

8 6

2. Determine the rule that produces the following outputvalues from the given input values.

Think and Discuss

3. Explain the relationship between the input values, a rule,and the output values.

4. Discuss whether the output values have to be different fromthe input values.

Georgia Performance

Standards

M8A1.b, M8A3.b,M8A3.c, M8A3.d,M8A3.i

Review for MasteryFunctions3D

LESSON

From a given rule for a relation, you can write a table of values.

Choose convenient x-values (domain or input).Get corresponding y-values (range or output).

y � 2x � 1

Write a table of values for each function and graph.

1. y � x � 1

2. y � 2x � 1

x 2x � 1 y�2 2(�2) � 1 � �5 �5

�1 2(�1) � 1 � �3 �3

0 2(0) � 1 � �1 �1

1 2(1) � 1 � 1 1

2 2(2) � 1 � 3 3

x

O 44

44

22

22�22

�����22

��44

�44

y

22

x

O 44

44

22

22�22

��22

��44

�44

y

x x � 1 y

�2 �2 � 1 � �3 �3

�1 �1 � 1 �

0 � 1 �

1 � 1 �

2 � 1 �

x

O 44

44

22

22�22

�����22

��44

�44

y

x 2x � 1 y

�2 2( ) � 1 �

�1

0

1

2

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Name Date Class

2 N D P R I N T

Copyright © by Holt, Rinehart and Winston. 83 Holt MathematicsAll rights reserved.

A function has exactly one output for each input. You can check tosee if a relation is a function by making sure each value in thedomain is associated with only one value in the range. You can usethe vertical line test on a graph.

Determine if the relation is a function. Explain.

Review for MasteryFunctions (continued)3D

LESSON

The relation is a function.Each x value has only one y value.

The relation is not a function.A vertical line intersects the graph attwo points.

1.

3.

2.

4.

Name Date Class

x y

1 10

2 20

3 30

4 40

5 50

O

2

�3

x

y

2 4

Determine if the relation is a function. Explain.

x y

�2 5

�1 7

0 9

�1 6

�2 4

O x

y

O

4

2

x

y

2 4

x y

1 1

2 1

3 1

4 1

5 1

Copyright © by Holt, Rinehart and Winston. 84 Holt MathematicsAll rights reserved.

Name Date Class

1. y � 3x � 4

2. y � 2x 2 � 1

Complete the table and graph each function.

Homework and PracticeFunctions3D

LESSON

y

xO�4 �2

�2

�4

�6 2

2

4

6

4 6

y

xO�4 �2

�2

�6 2

2

4

6

4 6

x 3x � 4 y

�3

�2

�1

0

1

x 2x 2 � 1 y

�2

�1

0

1

2

Determine if each relationship represents a function.

3. y 2 � 4x � 3 4.

5. For each function, find f (0), f (�1), and f (2).

6. Given the function f (x) � �4x 2 � 5 and the domain{ �3, �2, �1, 0, 1, 2, 3}. Find the range of the function.

Function f (0) f (�1) f (2)

y � �5x � 2

y � 3x 2 � 8

x 2 4 6 8y �1 �2 �3 �4

9–14.

15.

16. 20 patients

Exploration 3C1. Greg is multiplying each number by 2.

2. Yes; any number Mila gives will have onlyone output, the input multiplied by 2.

3. No; Greg’s rule cannot be a functionbecause two different outputs are givenfor one input.

4. relation

5. If Greg uses a relation, then the outputsfor Mila’s numbers are not necessarilyunique. If Mila gets different answers forthe same input, she cannot guess therule Greg is using.

Review for Mastery 3C1. {–1, –2, –3}; {1, 3, 5}

2. {a, b, c}; {1, 2, 3}

3. Yes; each domain value is assignedexactly 1 range value.

4. No; a is assigned to both d and e.

Homework and Practice 3C1. domain: {0, 1, 2}; range: {4, 5, 6}

2. domain: {–3, –2, –1}; range: {0, 3, 6}

3. Yes; m has one partner, 1, and n hasone partner, 0.

4. No; f has two partners, 10 and 12.

5. Yes; a has one partner, –3, and b hasone partner, –3.

6. No; –1 has two partners, c and d.

7. No; 1 has two partners, 4 and 10.

8. Yes; each value in the range has onepartner.

Exploration 3D1.

2.

3. An input value is substituted into a rule,evaluated, and the result is the outputvalue.

4. No, they can be the same.

x x � 2 y

2 2 � 2 � 0 0

4 4 � 2 � 2 2

6 6 � 2 � 4 4

8 8 � 2 � 6 6

x 2000 � 25x y

0 2000 � 25(0) � 2000 2000

1 2000 � 25(1) � 1975 1975

2 2000 � 25(2) � 1925 1950

3 2000 � 25(3) � 1900 1926

6

5

4

3

2

1

0 1 2 3 4 5 6

y

x

x 2x y (x, y)

1 2 2 (1, 2)

2 4 4 (2, 4)

3 6 6 (3, 6)

B

F

C

D

E

y

xO

�2

�4

2

�2�4

4

2 4

A

Copyright © by Holt, Rinehart and Winston. 14 Holt MathematicsAll rights reserved.

Answer Key

Copyright © by Holt, Rinehart and Winston. 15 Holt MathematicsAll rights reserved.

Review for Mastery 3D1.

2.

3. Not a function; domain values –2 and –1have two range values each.

4. Function; passes vertical line test.

5. Not a function; a vertical line at x � 0hits more than one point.

6. Function; domain values each have onlyone range value.

Homework and Practice 3D1.

2.

3. no

4. yes

5.

6. {–41, –21, –9, –5}

Function f(0) f(�1) f(1)

y � �5x � 2 2 7 �3

y � 3x 2 � 8 �8 �5 �5

y

xO�4 �2

�2

�6 2

2

4

6

4 6

x 2x 2 � 1 y

�2 2(�2)2 � 1 � 7 7

�1 2(�1)2 � 1 � 1 1

0 2(0)2 � 1 � �1 �1

1 2(1)2 � 1 � 1 1

2 2(2)2 � 1 � 7 7

y

xO�4 �2

�2

�4

�6 2

2

4

6

4 6

x 3x � 4 y

�3 3(�3) � 4 � �5 �5

�2 3(�2) � 4 � �2 �2

�1 3(�1) � 4 � 1 1

0 3(0) � 4 � 4 4

1 3(1) � 4 � 7 7

x

O 4

4

2

2�2

�2

�4

�4

y

x 2x � 1 y

�2 2(�2) � 1 � �3 �3

�1 2(�1) � 1 � �1 �1

0 2(0) � 1 � 1 1

1 2(1) � 1 � 3 3

2 2(2) � 1 � 5 5

x

O 4

4

2

2�2

�2

�4

�4

y

x x � 1 y

�2 �2 � 1 � �3 �3

�1 �1 � 1 � �2 �2

0 0 � 1 � �1 �1

1 1 � 1 � 0 0

2 2 � 1 � 1 1

Answer Key