Section 2 1 Relations and Functions 1 Defining

Section 2. 1 Relations and Functions 1

Defining Relations and Functions 1. Relation: • {(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

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

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

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

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

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

Vertical Line Test 1. Use the vertical line test to determine if the following represents a function. 8

Function vs. Non-Function 9

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

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

Function Notation 1. 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

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Examples 7 – 9 • Find f(-3), f(0), and f(5). 7. f(x) = 3 x – 5 8. f(a) = 3/4 a – 1 9. f(y) = -1/5 y + 3/5 14

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 15