Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

Warm Up What three terms come next? 1. 9, 12, 15, 18, . . . 2. –8, –3, 2, 7, … 3. 9, 10, 12, 15, 19, … 21, 24, 27 12, 17, 22 24, 30, 37

Problem of the Day Sandra, Greg, and Michael team up for a competitive eating contest. If Sandra can eat 3 hot dogs per minute, Greg can eat 4 hot dogs per minute, and Michael can eat 5 hot dogs per minute, how long will it take them to eat a combined total of 100 hot dogs? 1 2 8 minutes

Learn to represent functions with tables, graphs, or equations.

Vocabulary relation domain range function independent variable vertical line test

A set of ordered pairs is a relation A set of ordered pairs is a relation. The domain of a relation is the set of x-values of the ordered pairs. The range of a relation is the set of y-values of the ordered pairs. A function is a special type of relation that pairs each input, or domain value, with exactly one output, or range value.

Some functions can be written as equations in two variables Some functions can be written as equations in two variables. The independent variable represents the input of a function. The dependent variable represents the ouput of a function.

Additional Example 1: Finding Different Representations of a Function Make a table and a graph of y = 3 – x2. Make a table of inputs and outputs. Use the table to make a graph. 2 1 –1 –2 y 3 – x2 x 3 – (–2)2 –1 3 – (–1)2 2 3 – (0)2 3 3 – (1)2 2 3 – (2)2 –1

Make a table and a graph of y = x + 1. Check It Out: Example 1 Make a table and a graph of y = x + 1. Make a table of inputs and outputs. Use the table to make a graph. x y 2 3 –3 2 1 –1 y x + 1 x –1 + 1 0 + 1 1 1 + 1 2 2 + 1 3

Because a function has exactly one output for each input, you can use the vertical line test to test whether a graph is a function. If no vertical line intersects the graph at more than one point, then the relation is a function. If any vertical line intersects the graph at more than one point, the the relation is not a function.

Additional Example 2A: Identifying Functions Determine if the relationship represents a function. x 2 3 3 2 y 3 4 5 6 The input x = 2 has two outputs, y = 3 and y = 6. The input x = 3 also has more than one output. The relationship is not a function.

Additional Example 2B: Identifying Functions Determine if the relationship represents a function. The input x = 0 has two outputs, y = 2 and y = –2. Other x-values also have more than one y-value. The relationship is not a function.

Additional Example 2C: Identifying Functions Determine if the relationship represents a function. y = x3 Make an input-output table and use it to graph y = x3. (2)3 = 8 2 (1)3 = 1 1 (0)3 = 0 (–1)3 = –1 –1 (–2)3 = –8 –2 y x Each input x has only one output y. The relationship is a function.

Determine if the relationship represents a function. Check It Out: Example 2A Determine if the relationship represents a function. x 0 1 2 3 y 0 1 2 3 Each input x has only one output y. The relationship is a function.

Determine if the relationship represents a function. Check It Out: Example 2B Determine if the relationship represents a function. x y Since the relationship is linear there can only be one output y for each input x. 2 -2 2 The relationship is a function. -2

Check It Out: Example 2C Determine if the relationship represents a function. y = x – 1 2 3 – 1 3 1 2 – 1 1 – 1 –1 0 – 1 y x – 1 x Each input x has only one output y. The relationship is a function.