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192 Chapter 2 Linear Equations in Two Variables and Functions Section 2.6 Introduction to Functions 1. Definition of a Function In this section, we introduce a special type of relation called a function. Definition of a Function Given a relation in x and y, we say “y is a function of x” if, for each element x in the domain, there is exactly one value of y in the range. Note: This means that no two ordered pairs may have the same first coordinate and different second coordinates. To understand the difference between a relation that is a function and a relation that is not a function, consider Example 1. Determining Whether a Relation Is a Function Determine which of the relations define y as a function of x. a. b. c. x y 1 2 3 4 x y 1 2 3 2 1 4 x y 1 2 3 3 4 1 2 Example 1 Solution: a. This relation is defined by the set of ordered pairs same x 511, 32, 11, 42, 12, 12, 13, 226 different y-values When there are two possible range elements: and Therefore, this relation is not a function. x 1, y 3 y 4. 511, 42, 12, 12, 13, 226 b. This relation is defined by the set of ordered pairs . Notice that no two ordered pairs have the same value of x but different values of y.Therefore, this relation is a function. c. This relation is defined by the set of ordered pairs 511, 42, 12, 42, 13, 426. Notice that no two ordered pairs have the same value of x but different values of y.Therefore, this relation is a function. Concepts 1. Definition of a Function 2. Vertical Line Test 3. Function Notation 4. Finding Function Values from a Graph 5. Domain of a Function


miller_intermediate_algebra_4e_ch1_3
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