5-2 Functions, Tables, and Graphs Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of...

5-2 Functions, Tables, and Graphs

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes


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


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

–


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

Sunshine State Standards


Vocabulary

function

input

output


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.


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.


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


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.


Input

y = 4x2

Rule Output

x 4x2 y

–5

0

5

4(–5)2

4(0)2

4(5)2

100

0

100


Check It Out: Example 1A

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


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


Check It Out: Example 1B

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


Input

y = 3x2

Rule Output

x 3x2 y

–2

0

5

3(–2)2

3(0)2

3(5)2

12

0

75


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.


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

Helpful Hint


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



(–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)



x

y


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


y = 6x2



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


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


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


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)


1. Identify the output for each input.

A. B.



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

A. B.


5-2 Functions, Tables, and Graphs Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of...

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