1. Relations and Functions
Section 2.1
Relations and Functions 1

2. Defining Relations and Functions
{(0,10), (0.1, 9.8), (0.2, 9.4), (0.3, 8.6), (0.4, 7.4), …}
Domain: {0, 0.1, 0.2, 0.3, 0.4,…}
Range: {10, 9.8, 9.4, 8.6, 7.4,…} 2

3. Defining Relations and Functions
Definition 1: A relation is a set of ordered pairs.
Definition 2: The domain is the set of all first numbers in each pair, or the x-values.
Definition 3: The range is the set of all second numbers in each pair, or y-values. 3

4. Example 1
Graph the relation {(-2, 4), (3, -2), (-1, 0), (1, 5)}. 4

5. Example 2
Find the domain and range of the relation.

6. Defining Relations and Functions
Definition 4: When each element of the domain has only one element associated with it in the range, the relation is called a function. 6

7. Examples 3 & 4
Determine whether the following relations are functions.

8. Vertical Line Test
Use the vertical line test to determine if the following represents a function. 8

9. Function vs. Non-Function9

10. Function vs. Non-Function
Determine if each relation is a function.
y = 2x + 7
{(1, 2), (2, 3), (3, 4), (4, 3), (3, 2)} 10

11. Examples 5 & 6:
Use the vertical line test to determine if the following represents a function.

12. Function Notation
The f(x) notation is called function notation. When the value of the independent variable x is 3, f(3) represents the value of the function. 12

13. 13

14. Examples 7 – 9 Find f(-3), f(0), and f(5). f(x) = 3x – 5
f(a) = 3/4a – 1
f(y) = -1/5y + 3/5

15. TOTD Determine whether each relation is a function. Explain or show.
{(1, 1), (2, 2), (3, 5), (4, 10), (5, 5)
For the following function, find f(-5), f(-3), f(1/2), and f(4).
f(x) = -x – 7