Relations and Functions

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Presentation transcript:

Relations and Functions Section 2.1 Relations and Functions 1

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

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.

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.

Vertical Line Test 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 = 2x + 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.

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

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

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