tell whether the pairing is a function. identify a function example 2 a. a. the pairing is not a...

Tell whether the pairing is a function.

Identify a functionEXAMPLE 2

a.

The pairing is not a function because the input 0 is paired with both 2 and 3.

b.

Identify a functionEXAMPLE 2

OutputInput

21

0 0

4 8

6 12

The pairing is a function because each input is pairedwith exactly one output.

SOLUTION

GUIDED PRACTICE for Example 2

Tell whether the pairing is a function.

1221Output

12963Input2.

369

12

1221

The pairing is a function because each input is pairedwith exactly one output.

SOLUTION

GUIDED PRACTICE for Example 2

Tell whether the pairing is a function.

3210Output

7422Input3.

The pairing is not a function because each input is notpaired with exactly one output.

2

47

0123

SOLUTION

GUIDED PRACTICE for Example 1

1. Identify the domain and range of the function.

Input 0 1 2 4Output 5 2 2 1

The domain is the set of inputs: 0, 1, 2, and 4

The range is the set of outputs: 1, 2, and 5

Write a function ruleEXAMPLE 4

Write a rule for the function. Input

Output 2

1

6 123

4

8

60 10

SOLUTION

and let y or dependent variable. Notice that eachbe the output,

Let x be the input, or independent variable,

output is 2 more than the corresponding input. So, a rule for the function is y = x + 2.

Write a function rule for a real-world situationEXAMPLE 5

Concert Tickets

You are buying concert tickets that cost $15 each. You can buy up to 6 tickets. Write the amount (in dollars) you spend as a function of the number of tickets you buy.Identify the independent and dependent variables.Then identify the domain and the range of the function.

Write a function rule for a real-world situationEXAMPLE 5

SOLUTION

So, the function rule is A = 15n. The amount spent depends on the number of tickets bought, so n is the independent variable and A is the dependent variable.

Write a verbal model. Then write a function rule. Let n represent the number of tickets purchased and A represent the amount spent (in dollars).

A 15 n=

Amount spent

(dollars)

Cost per ticket

(dollars/ticket)

Tickets purchased

(tickets)= •

Write a function rule for a real-world situationEXAMPLE 5

Because you can buy up to 6 tickets, the domain of the function is 0, 1, 2, 3, 4, 5, and 6. Make a table to identify the range.

Amount (dollars), A

0 1 32 654

0 15 4530 7560 90

Number of tickets, n

The range of the function is 0, 15, 30, 45, 60, 75, and 90.

Graph a function

EXAMPLE 1

STEP 2 Plot a point for each ordered pair (x, y).

STEP 2

Plot the points

EXAMPLE 2Graph a function

Replacement Set

• {0,1,2,5} is the replacement set for inputs for f(x)=2x+1

• What is the replacement set for outputs?

Evaluate Functions

• Evaluate f(x)=x2+1 for • f(4)• F(10)

Linear vs. Quadratic

• Graphs as a _____• Power of x is ___• _____is constant

• Graphs as a _____• Power of x is _____• _____ is not constant

but is changing at a constant rate

Linear vs. Quadratic

inputs outputs

0 15

1 21

2 27

3 33

4 39

5 45

x

Inputs outputs

0 5

1 6

2 9

3 14

4 21

5 30

x

Is it linear, quadratic or neither?

inputs outputs

0 -2

1 -1

2 2

3 7

4 14

inputs outputs

0 4

1 2

2 -4

3 -6

4 -10

inputs outputs

0 -5

1 -4

2 -1

3 0

4 1

inputs outputs

0 -1

1 4

2 9

3 14

4 19

inputs outputs

0 9

1 10

2 13

3 18

4 25

inputs outputs

0 7

1 5

2 3

3 1

4 -1

RESET CALCULATOR

• GO TO MEMORY (2ND THEN +)

• SELECT RESET (7)• ALL RAM (1)• RESET (2)

How to plot points on calculator

• Enter Data into Lists

• Turn Stat Plot On

• Window or ZoomStat

• Calculator goes here

Linear Regression

• Press STAT• Go To CALC• Select 4 for linear

regression• Press Enter• Input into y=• Graph

Quadratic Regression

• Press STAT• Go To CALC• Select 5 for quadratic

regression• Press Enter• Input into y=• Graph