1. Functions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. Functions 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

3. Functions 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? 8 minutes 1212

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

5. Functions Vocabulary relation domain range function independent variable dependent variable vertical line test

6. Functions 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.

7. Functions

9. 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.

10. Functions Make a table and a graph of y = 3 – x 2. Additional Example 1: Finding Different Representations of a Function Make a table of inputs and outputs. Use the table to make a graph. 2 1 0 –1 –2 y3 – x 2 x 3 – (–2) 2 3 – (–1) 2 3 – (0) 2 3 – (1) 2 3 – (2) 2 –1 2 3 2

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

12. Functions 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.

13. Functions Determine if the relationship represents a function. Additional Example 2A: Identifying Functions 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. x 2 3 3 2 y 3 4 5 6

14. Functions Determine if the relationship represents a function. Additional Example 2B: Identifying Functions 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.

15. Functions Determine if the relationship represents a function. y = x 3 Additional Example 2C: Identifying Functions Each input x has only one output y. The relationship is a function. (2) 3 = 82 (1) 3 = 11 (0) 3 = 00 (–1) 3 = –1–1 (–2) 3 = –8–2 yx Make an input-output table and use it to graph y = x 3.

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

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

18. Functions Determine if the relationship represents a function. y = x – 1 Check It Out: Example 2C Each input x has only one output y. The relationship is a function. 23 – 13 12 – 12 01 – 11 –10 – 10 yx – 1x

19. Functions Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

20. Functions Lesson Quiz: Part I 1. Graph the function y = x 2 – 3.

21. Functions Lesson Quiz: Part II Determine if each relationship represents a function. 2. 3. y = 3x + 5 no yes

22. Functions 1.Identify the graph of the function y = x 2 – 4. A. C. B. D. Lesson Quiz for Student Response Systems

23. Functions 2.Identify the relationship that represents a function. A. C. B. D. Lesson Quiz for Student Response Systems

24. Functions 3. Identify the relationship that represents a function. A. y 2 = 4 B. y = 2x C. y 2 = 9 D. y 2 = 16 Lesson Quiz for Student Response Systems