• independent variable

• dependent variable

• vertical line test

• function notation

Relation: a set of ordered pairs

Domain: the set of x values of the relationRange: the set of y values of the relation

Function: a relation in which each member of of the domain is paired with one and only one member of the range

Methods of testing for a function:

Inspect the ordered pairs. If each x is different it is a function. If 2 x values are thesame, it is not a function.

Vertical line test: Look at the graph of therelation. If every point is on a separate vertical line, it is a function. If 2 or morepoints are on the same vertical line, it is nota function.

Determine Whether a Relation is a Function

A. Determine whether the relation is a function. Explain.

(3, 48), (7, 21), (5, 15), (1, 13), (2, 12)

Determine Whether a Relation is a Function

B. Determine whether the relation is a function. Explain.

A. A

B. B

C. C

D. D

A. Determine whether the relation is a function. Explain. {(1, 5), (–2, 7), (3, 8), (4, 5)}

A. A

B. B

C. C

D. D

B. Determine whether the relation is a function. Explain.

Use a Graph to Identify Functions

Determine whether the graph is a function. Explain your answer.

A. A

B. B

C. C

D. D

Determine whether the graph is a function. Explain.

Function Notation: f(x) =

Examples: f(x) = 2x + 3

g(x) = x2

Find a Function Value

A. If f(x) = 6x + 5, what is the function value of f(5)?

Find a Function Value

B. If f(x) = 6x + 5, what is the function value of f(–4)?

A. A

B. B

C. C

D. D

A. If f(x) = 2x – 7, what is the value of f(4)?

A. A

B. B

C. C

D. D

B. If f(x) = 2x – 7, what is the value of f(–3)?

Use Function Notation

A. GREETING CARDS Ms. Newman spent $8.82 buying cards that sold for $0.49 each. Use function notation to write an equation that gives the total cost as a function of the number of cards purchased.

Answer: t(c) = 0.49c

Use Function Notation

B. GREETING CARDS Ms. Newman spent $8.82 buying cards that sold for $0.49 each. Use the equation to determine the number of cards purchased.

t(c) = 0.49c Write the function.

8.82 = 0.49c Replace t(c) with 8.82.

18 = c Divide each side by 0.49.

Answer: So, Mrs. Newman bought 18 cards.

A. A

B. B

C. C

D. D

A. CANDY BARS Erik bought candy bars that cost $0.59 cents each. Which function describes his purchase if t(c) = total cost and c = the number of candy bars?

A. A

B. B

C. C

D. D

B. CANDY BARS Erik bought candy bars that cost $0.59 cents each and spent $4.72. If t(c) = total cost and c = the number of candy bars, use the function t(c) = 0.59c to find the number of candy bars purchased.