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

2. 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. 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

4. I know that in a function, for every “x” there is exactly one “y”.
I can use the vertical line test to determine whether a graph is a function.

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

16. 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.

26. 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.

27. 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

28. 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

37. 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.

40. Additional Example 2A: Identifying Functions
Determine if the relationship represents a function. x y
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.

41. 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.

42. 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.

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

44. 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

45. 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.

46. Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems

47. Lesson Quiz: Part I
1. Graph the function y = x2 – 3.

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

49. Lesson Quiz for Student Response Systems
Identify the graph of the function
y = x2 – 4. C. D.

50. Lesson Quiz for Student Response Systems
2. Identify the relationship that represents a function. C. D.

51. Lesson Quiz for Student Response Systems
3. Identify the relationship that represents a function.
A. y2 = 4
B. y = 2x
C. y2 = 9
D. y2 = 16