1. 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

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

3. Vocabulary
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.

5. 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.

6. Representations of a Function
Example 1
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

7. Make a table and a graph of y = x + 1.
You Try
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

8. If 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.

9. Identifying Functions: Graph
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.

10. Identifying Functions: Table
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.

11. Identifying Functions: Equation
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.

12. Determine if the relationship represents a function.
You Try Dtermining: a
Determine if the relationship represents a function. x y
Each input x has only one output y.
The relationship is a function.

13. Determine if the relationship represents a function.
You Try Determining: b
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

14. You Try Determining: c
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.