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Section 3.3 Functions 179 Objective 1 Examples Determine if each relation is a function. If not, explain why. Grade Student A Dylan, Hunter B Angela, Edward C Aretha, Ginger D Jake F Natalia 1a. {(-4, 0), (-3, 2), (-3, -2), (0, 4), (0, -4)} 1b. {(-2, -3), (-1, -3), (0, -3), (1, -3), (2, -3), (3, 3)} 1c. Let the relation be defined by the given table, where x is the math grade and y is the student earning the grade. 1d. x = y2 Solutions 1a. –4 –2 0 2 4 –4 –3 0 Write the relation as a mapping. The x-value of -3 corresponds to 2 y-values, 2 and -2. The x-value of 0 correspond to 2 y-values, -4 and 4. So, the relation is not a function. 1b. Write the relation as a mapping. –3 –2 –1 0 1 2 3 Each x-value corresponds to only 1 y-value So, the relation is a function. 1c. The relation is not a function since the grades of A, B, and C each correspond to more than 1 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. 1d. We must determine how many output values correspond to a given input. x = y2 4 = y2 Let x = 4, for example. y = 2 or y = -2 Note that 4 = (2)2 and 4 = (-2)2. Since (4, 2) and (4, -2) are solutions of this equation, there is an input value that corresponds to 2 output values. So, this equation is not a function. Student Check 1 Determine if each relation is a function. If not, explain why. a. 5(5, 1), (5, -2), (5, 6), (5, 3), (5, 0)6 b. 5(1, 5), (-2, 5), (6, 5), (3, 5), (0, 5)6 c. Let the relation be defined by the given mapping, where x is the student and y is the grade earned in math class. d. y = x2 Student Grade t t t


hendricks_intermediate_algebra_1e_ch1_3
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