Over Chapter 7 A.A B.B C.C D.D 5-Minute Check 6 A.26 B.52 C.78 D.156 The circle graph shows the results of a middle school survey about favorite lunch foods. Suppose 650 students were surveyed. How many more students favor salad than hoagies?

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Then/Now You have already learned how to find function rules and create function tables. (Lesson 1–5) Determine whether a relation is a function. Write a function using function notation.

Vocabulary independent variable dependent variable vertical line test function notation The variable in a function with a value that is subject to choice (you pick it) The variable in a relation with a value that depends on the value of the independent variable If any vertical line drawn on the graph of a relation passes through no more than one point on the graph for each value of x in the domain, then the relation is a function A way to name a function that is defined by an equation. In function notation, the equation y=3x-8 is written as f(x) = 3x - 8

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)  Answer: Yes; this is a function because each x-value is paired with only one y-value.

Example 1B Determine Whether a Relation is a Function B. Determine whether the relation is a function. Explain. Answer: No; this is not a function because 3 in the domain is paired with more than one value in the range.

A.A B.B C.C D.D Example 1 CYP A A.It is a function because each x-value is paired with only one y-value. B.It is a function because each y-value is paired with only one x-value. C.It is not a function because an x-value is paired with more than one y-value. D.It is not a function because a y-value is paired with more than one x-value. 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. A.It is a function because each x-value is paired with only one y-value. B.It is a function because each y-value is paired with only one x-value. C.It is not a function because an x-value is paired with more than one y-value. D.It is not a function because a y-value is paired with more than one x-value.

Example 2 Use a Graph to Identify Functions Determine whether the graph is a function. Explain your answer. Answer: No; The graph is not a function because it does not pass the vertical line test. When x = 7, there are two different y-values.

A.A B.B C.C D.D Example 2 Determine whether the graph is a function. Explain. A.It is a function because each domain value is paired with only one range value. B.It is a function because each range value is paired with only one domain value. C.It is not a function because a domain value is paired with more than one range value. D.It is not a function because a range value is paired with more than one domain value.

Example 3A Find a Function Value A. If f(x) = 6x + 5, what is the function value of f(5)? f(x)=6x + 5Write the function. f(5)=6 ● 5 + 5Replace x with 5. f(5)=35Simplify. Answer:35

Example 3B Find a Function Value B. If f(x) = 6x + 5, what is the function value of f(–4)? f(x)=6x + 5Write the function. f(–4)=6 ● (–4) + 5Replace x with –4. f(–4)=–19Simplify. Answer:–19

A.A B.B C.C D.D Example 3 CYP A A.–5 B.–1 C.1 D.5 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 A.–13 B.–10 C.10 D.13 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.t(c) = 0.59c B.c = 0.59 ● t(c) C.t(c) = c D.c = t(c) 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 A.5 candy bars B.6 candy bars C.8 candy bars D.9 candy bars 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.

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