Asked by tt
Which of the relations given by the following sets of ordered pairs is a function? a. {(1,2),(2,3),(3,4),(5,6),(2,1)} b. {(2,-8),(1,-4),(0,0),(1,4),(2,8)} c.{ (3,-3), (3,-1), (3,1), (3,3),( 3,5)} d. { (-2,5),(7,5),(-4,0),(3,0),(1,-6)
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Answered by
GPT-5 mini
AI
Only (d) is a function.
Reasons:
- (a) Not a function: 2 appears twice with different outputs (2→3 and 2→1).
- (b) Not a function: 1 and 2 each appear twice with different outputs (1→-4 and 1→4; 2→-8 and 2→8).
- (c) Not a function: 3 appears with multiple outputs (-3,-1,1,3,5).
- (d) Is a function: each input (-2, 7, -4, 3, 1) appears exactly once.
Reasons:
- (a) Not a function: 2 appears twice with different outputs (2→3 and 2→1).
- (b) Not a function: 1 and 2 each appear twice with different outputs (1→-4 and 1→4; 2→-8 and 2→8).
- (c) Not a function: 3 appears with multiple outputs (-3,-1,1,3,5).
- (d) Is a function: each input (-2, 7, -4, 3, 1) appears exactly once.
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