12-1 Introduction to Functions

Course 2

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Warm UpSolve.

1. x + 4 = 19

2. y – 2.3 = 7.8

3. 4z = 120

4. = 8

x = 15

y = 10.1

z = 30

Course 2

12-1 Introduction to Functions

w9 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

–

Course 2

12-1 Introduction to Functions

Learn to use function tables to generate and graph ordered pairs.

Course 2

12-1 Introduction to Functions

Vocabulary

function

Insert Lesson Title Here

Course 2

12-1 Introduction to Functions

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 a single output value for each input value.

A function can be represented as a rule written in words, such as “double the number and add nine to the result.”

Course 2

12-1 Introduction to Functions

A function can also be represented by an equation with two variables. One variable represents the input, and the other represents the output.

Rule

Output

InputYou can use a table to organize the input and output values of a function. Your table may show as many possible input and output values as you choose

Course 2

12-1 Introduction to Functions

Additional Example 1A: Completing a Function Table

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

Find the output for each input.

Input

A. y = 8x + 5

Rule Output

x 8x + 5 y

–4

–2

1

8(–4) + 5

8(–2) + 5

8(1) + 5

–27

–11

13

Course 2

12-1 Introduction to Functions

Additional Example 1B: Completing a Function Table

Substitute –3 for x and simplify.Substitute 0 for x and simplify.Substitute 4 for x and simplify.

Find the output for each input.

Input

B. y = 4x2

Rule Output

x 4x2 y

–3

0

4

4(–3)2

4(0)2

4(4)2

36

0

64

Course 2

12-1 Introduction to Functions

Try This: Example 1A

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

Find the output for each input.

Input

A. y = 5x + 3

Rule Output

x 5x + 3 y

–6

–3

3

5(–6) + 3

5(–3) + 3

5(3) + 3

–27

–12

18

Course 2

12-1 Introduction to Functions

Try This: Example 1B

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

Find the output for each input.

Input

B. y = 3x2

Rule Output

x 3x2 y

–2

0

5

3(–2)2

3(0)2

3(5)2

12

0

75

Course 2

12-1 Introduction to Functions

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.

Course 2

12-1 Introduction to Functions

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

Helpful Hint

Course 2

12-1 Introduction to Functions

Make a function table 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

A. y = 3x – 4

(–2, –10)

(–1, –7)

(0, –4)

(1, –1)

(2, 2)

Course 2

12-1 Introduction to Functions

Additional Example 2B: Graphing Functions with Ordered Pairs

B. y = 5x2

Make a function table and graph the resulting ordered pairs.

RuleInput Output OrderedPair

5(–2)2

x 5x2 y

(–2, 20)–2

–1

0

1

2

5(–1)2

5(0)2

5(1)2

5(2)2

20

5

0

5

20

(–1, 5)

(0, 0)

(1, 5)

(2, 20)

(x, y)

x

16

20

4 8–8

12

8

O

4

–4

(0,0)

(–1, 5) (1, 5)

(2, 20)y

(–2, 20)

Course 2

12-1 Introduction to Functions

Make a function table 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

A. y = 2x – 3

(–2, –7)

(–1, –5)

(0, –3)

(1, –1)

(2, 1)

Try This: Example 2A

Course 2

12-1 Introduction to Functions

B. y = 6x2

Make a function table 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)

Try This: Example 2B

Course 2

12-1 Introduction to Functions

Lesson Quiz: Part 1

Find the output for each input value.

Insert Lesson Title Here

Input Rule Output

4x – 1 yx

–2

0

4

–9

–1

15

Course 2

12-1 Introduction to Functions

Lesson Quiz: Part 2

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

Insert Lesson Title Here

Possible answer:

x y

–2 3

0 –1

2 3

x

y

–2

–2

2

2–4

–4

4

4(–2, 3) (2, 3)

(0, –1)

Course 2

12-1 Introduction to Functions