Section 3.6 Functions 267 Functions We defined a relation as a set of ordered pairs—a correspondence between a set of inputs and outputs. A function is a special type of relation. ������������������������ A function is a relation in which each member of the domain (or each input) corresponds to exactly one member of the range (or an output). In other words, each input, or x-value, can have only one output, or y-value. In the opening of this section, we mentioned a student ID that corresponds to more than one output. It corresponds to the student who was trying to register as well as to the other student whose name appeared on the screen. This was certainly due to entry error. It doesn’t make sense for a student ID to correspond to more than one student. Except in the case of an error, this relation is a function. Each input (student ID) can only correspond to one output (student). ���������������������� Determining if a Relation Is a Function Step 1: Determine how many y-values correspond to each x-value. a. If there is only one corresponding y-value for each x-value, then the relation is a function. b. If at least one x-value corresponds to more than one y-value, then the relation is not a function. �� ������������������������ ������������������ Determine if each relation is a function. If not, explain why. 2a. {(-4, 0), (-3, 2), (-3, -2), (0, 4), (0, -4)} 2b. {(-2, -3), (-1, -3), (0, -3), (1, -3), (2, -3), (3, -3)} 2c. Let the relation be defined by the mapping, where x is the math grade and y is the student earning the grade. Grade Student A B C D F Angela Aretha Dylan Edward Ginger Hunter Natalia 2d. y = uxu Solutions 2a. This is not a function since the x-value of -3 corresponds to two y-values, 2 and -2. Also, the x-value of 0 corresponds to two y-values, -4 and 4. 2b. This is a function since each x-value corresponds to only one y-value. 2c. This is not a function since the grade of A, B, and C correspond to more than one student. For example, the grade of A corresponds to Dylan and Hunter. The grade of B corresponds to Angela and Edward. The grade of C corresponds to Aretha and Ginger. 2d. This is a function since each input, or x-value, has only one possible output, or y-value. When a value is substituted for x, there is only one possible y-value. Some examples are x=-3; y = u-3u = 3S(-3, 3) x = 2; y = u2u = 2S(2, 2) Objective 2 ▶ Determine if a relation is a function.
hendricks_beginning_algebra_1e_ch1_3
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