5-2 Functions, Tables, and Graphs

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

5-2 Functions, Tables, and Graphs

Warm UpSolve.

1. x + 4 = 19

2. y – 2.3 = 7.8

3. 4z = 120

4. = 8

x = 15

y = 10.1

z = 30w9 w = 72

5-2 Functions, Tables, and Graphs

Problem of the Day

Substitute the numbers 1, 2, and 3 for the letters a, b, and c in such a way that the number sentence is correct.

a = 2, b = 3, c =1

1aa

+ 1ab = 1

ac

1ab

–

5-2 Functions, Tables, and Graphs

Prep for MA.7.A.1.4 Graph proportional relationships…Review of MA.6.A.3.6

Sunshine State Standards

5-2 Functions, Tables, and Graphs

Vocabulary

function

input

output

5-2 Functions, Tables, and Graphs

Rube Goldberg, a famous cartoonist, invented machines that perform ordinary tasks in extraordinary ways. Each machine operates according to a rule, or a set of steps, to produce a particular output.

In mathematics, a function operates according to a rule to produce exactly one output value for each input value. The input is the value substituted into the function. The output is the value that results from the substitution of a given input into the function.

5-2 Functions, Tables, and Graphs

Function Rule

Outputvariable

Input variable

You can use a table to organize and display the input and output values of a function.

A function can be represented as a rule written in words, such as “double the number and add nine to the result,” or by an equation with two variables. One variable represents the input, and the other represents the output.

5-2 Functions, Tables, and Graphs

Additional Example 1A: Completing a Function Table

Substitute –4 for x. Then simplify.Substitute –2 for x. Then simplify.Substitute 1 for x. Then simplify.

Find the output for each input.

Input

y = 8x + 5

Rule Output

x 8x + 5 y

–4

–2

1

8(–4) + 5

8(–2) + 5

8(1) + 5

–27

–11

13

5-2 Functions, Tables, and Graphs

Additional Example 1B: Completing a Function Table

Substitute –5 for x. Then simplify.Substitute 0 for x. Then simplify.Substitute 5 for x. Then simplify.

Find the output for each input.

Input

y = 4x2

Rule Output

x 4x2 y

–5

0

5

4(–5)2

4(0)2

4(5)2

100

0

100

5-2 Functions, Tables, and Graphs

Check It Out: Example 1A

Substitute –6 for x. Then simplify.Substitute –3 for x. Then simplify.Substitute 3 for x. Then simplify.

Find the output for each input.

Input

y = 5x + 3

Rule Output

x 5x + 3 y

–6

–3

3

5(–6) + 3

5(–3) + 3

5(3) + 3

–27

–12

18

5-2 Functions, Tables, and Graphs

Check It Out: Example 1B

Substitute –2 for x. Then simplify.Substitute 0 for x. Then simplify.Substitute 5 for x. Then simplify.

Find the output for each input.

Input

y = 3x2

Rule Output

x 3x2 y

–2

0

5

3(–2)2

3(0)2

3(5)2

12

0

75

5-2 Functions, Tables, and Graphs

An ordered pair is a pair of numbers that represents a point on a graph.

Remember!

You can also use a graph to represent afunction. The corresponding input and output values together form unique ordered pairs.

5-2 Functions, Tables, and Graphs

When writing an ordered pair, write the input value first and then the output value.

Helpful Hint

5-2 Functions, Tables, and Graphs

Make a function table for x = –2, –1, 0, 1, and 2, and graph the resulting ordered pairs.

Additional Example 2A: Graphing Functions Using Ordered Pairs

x

y

RuleInput Output OrderedPair

3(–2) – 4

x 3x – 4 y

(–2, –10)

2

4

–2

–1

0

1

2

3(–1) – 4

3(0) – 4

3(1) – 4

3(2) – 4

–10

–7

–4

–1

2

(–1, –7)

(0, –4)

(1, –1)

(2, 2)

(x, y)2 4–2

–2

–4

–10

–6

–8

–4

y = 3x – 4

(–2, –10)

(–1, –7)

(0, –4)

(1, –1)

(2, 2)

5-2 Functions, Tables, and GraphsAdditional Example 2B: Graphing Functions Using

Ordered Pairs

y = x2 + 1

Make a function table for x = –2, –1, 0, 1, and 2, and graph the resulting ordered pairs.

RuleInput Output OrderedPair

(–2)2 + 1

x x2 + 1 y

(–2, 5)–2

–1

0

1

2

(–1)2 + 1

(0)2 + 1

(1)2 + 1

(2)2 + 1

5

2

1

2

5

(–1, 2)

(0, 1)

(1, 2)

(2, 5)

(x, y)

x2 4–4

6

4

O

2

–2(0,1)

(–1, 2) (1, 2)

(2, 5)

y

(–2, 5)

5-2 Functions, Tables, and Graphs

Make a function table for x = –2, –1, 0, 1, and 2, and graph the resulting ordered pairs.

x

y

RuleInput Output OrderedPair

2(–2) – 3

x 2x – 3 y

(–2, –7)

2

4

–2

–1

0

1

2

2(–1) – 3

2(0) – 3

2(1) – 3

2(2) – 3

–7

–5

–3

–1

1

(–1, –5)

(0, –3)

(1, –1)

(2, 1)

(x, y)2 4–2

–2

–4

–10

–6

–8

–4

y = 2x – 3

(–2, –7)

(–1, –5)

(0, –3)

(1, –1)

(2, 1)

Check It Out: Example 2A

5-2 Functions, Tables, and Graphs

y = 6x2

Make a function table for x = –2, –1, 0, 1, and 2, and graph the resulting ordered pairs.

RuleInput Output OrderedPair

6(–2)2

x 6x2 y

(–2, 24)–2

–1

0

1

2

6(–1)2

6(0)2

6(1)2

6(2)2

24

6

0

6

24

(–1, 6)

(0, 0)

(1, 6)

(2, 24)

(x, y)

x

16

20

4 8–8

12

8

O

4

–4(0,0)

(–1, 6) (1, 6)

(2, 24)y

(–2, 24)

Check It Out: Example 2B

5-2 Functions, Tables, and Graphs

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

5-2 Functions, Tables, and Graphs

Lesson Quiz: Part I

1. Find the output for each input value.

Input Rule Output

4x – 1 yx

–2

0

4

–9

–1

15

4(–2) – 1

4(0) – 1

4(4) – 1

5-2 Functions, Tables, and Graphs

Lesson Quiz: Part II2. Make a function table with three input values for y = x2 – 1, and graph the resulting ordered pairs.

Possible answer:

x

y

–2

–2

2

2–4

–4

4

4(–2, 3) (2, 3)

(0, –1)

Output Ordered Pair

RuleInput

x2 – 1 yx

–2

0

2

3

–1

322 – 1

–22 – 1

02 – 1

(x, y)

(–2, 3)

(0, –1)

(2, 3)

5-2 Functions, Tables, and Graphs

1. Identify the output for each input.

A. B.

Lesson Quiz for Student Response Systems

5-2 Functions, Tables, and Graphs

2. Identify a function table for y = x2 – 3, and graph the resulting ordered pairs.

A. B.

Lesson Quiz for Student Response Systems