1. Course 3 3-4 Functions 3-4 Functions Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

2. Course 3 3-4 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. Course 3 3-4 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. Course 3 3-4 Functions Learn to represent functions with tables, graphs, or equations.

5. Course 3 3-4 Functions Vocabulary function input output domain range vertical line test

6. Course 3 3-4 Functions A function is a rule that relates two quantities so that each input value corresponds to exactly one output value. The domain is the set of all possible input values, and the range is the set of all possible output values.

7. Course 3 3-4 Functions Functions can be represented in many ways, including tables, graphs, and equations. If the domain of a function has infinitely many values, it is impossible to represent them all in a table, but a table can be used to show some of the values and to help in creating a graph.

8. Course 3 3-4 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. x3 – x 2 y –2–2 –1–1 0 1 2 3 – (–2) 2 3 – (–1) 2 3 – (0) 2 3 – (1) 2 3 – (2) 2 –1 2 3 2

9. Course 3 3-4 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. xx + 1y –1 0 1 2 –1 + 1 0 + 1 1 + 1 2 + 1 0 1 2 3 x y 2 3 –3

10. Course 3 3-4 Functions If a relationship is a function, each input has exactly one output. When the relationship is graphed, use the vertical line test. Place a vertical line on the graph. If the line intersects the graph at only one point, then the relationship is a function. If the line intersects the graph at more than one point, then the relationship is not a function.

11. Course 3 3-4 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. xy 23 34 35 26 The relationship is not a function.

12. Course 3 3-4 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.

13. Course 3 3-4 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. xy –2(–2) 3 = –8 –1(–1) 3 = –1 0(0) 3 = 0 1(1) 3 = 1 2(2) 3 = 8 Make an input-output table and use it to graph y = x 3.

14. Course 3 3-4 Functions Determine if the relationship represents a function. Check It Out: Example 2A Each input x has only one output y. xy 00 11 22 33 The relationship is a function.

15. Course 3 3-4 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

16. Course 3 3-4 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. xx – 1y 00 – 1– 1 11 – 10 22 – 11 33 – 12

17. Course 3 3-4 Functions Lesson Quiz: Part I 1. Graph the function y = x 2 – 3. x y 2 2 -2 4 4-4

18. Course 3 3-4 Functions Lesson Quiz: Part II Determine if each relationship represents a function. 2. 3. y = 3x + 5 no yes