Vocabulary independent variable dependent variable vertical line test function notation

Relation: a set of ordered pairs Domain: the set of x values of the relation Range: 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 the same, it is not a function. Vertical line test: Look at the graph of the relation. If every point is on a separate vertical line, it is a function. If 2 or more points are on the same vertical line, it is not a function.

Example 1A 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) 

Example 1B Determine Whether a Relation is a Function B. Determine whether the relation is a function. Explain.

A.A B.B C.C D.D Example 1 CYP A 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 Example 1 CYP B B. Determine whether the relation is a function. Explain.

Example 2 Use a Graph to Identify Functions Determine whether the graph is a function. Explain your answer.

A.A B.B C.C D.D Example 2 Determine whether the graph is a function. Explain.

Function Notation: f(x) = Examples: f(x) = 2x + 3 g(x) = x 2

Example 3A Find a Function Value A. If f(x) = 6x + 5, what is the function value of f(5)?

Example 3B 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 Example 3 CYP A A. If f(x) = 2x – 7, what is the value of f(4)?

A.A B.B C.C D.D Example 3 CYP B B. If f(x) = 2x – 7, what is the value of f(–3)?

Example 4A 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

Example 4B 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)=0.49cWrite the function. 8.82=0.49cReplace t(c) with =cDivide each side by Answer:So, Mrs. Newman bought 18 cards.

A.A B.B C.C D.D Example 4 CYP A 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 Example 4 CYP B 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.