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Answer :
The correct answer is option B. The relation represented by B. X: -7, -5, -7, 2; Y: 34, 32, 40, 34 is NOT a function.
To determine whether a relation is a function, we must check if each x-value corresponds to exactly one y-value. This is known as the vertical line test in the context of graphs, where a vertical line should not intersect the graph at more than one point for the graph to represent a function.
Let's examine each option:
A. X: -7, -5, 7, 10; Y: 34, 32, 40, 34
Each x-value corresponds to a unique y-value, so this relation is a function.
B. X: -7, -5, -7, 2; Y: 34, 32, 40, 34
Here, the x-value -7 corresponds to two different y-values: 34 and 40. This violates the definition of a function, as a function must have exactly one y-value for each x-value.
C. X: -7, -5, -1, 2; Y: 34, 32, 40, 34
Each x-value corresponds to a unique y-value, so this relation is a function.
D. X: -7, -5, 7, 10; Y: 34, 32, 40, 34
Each x-value corresponds to a unique y-value, so this relation is a function.
The complete question is:
Which of the following represents a relation that is NOT a function?
A. X: -7, -5, 7, 10; Y: 34, 32, 40, 34
B. X: -7, -5, -7, 2; Y: 34, 32, 40, 34
C. X: -7, -5, -1, 2; Y: 34, 32, 40, 34
D. X: -7, -5, 7, 10; Y: 34, 32, 40, 34
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Rewritten by : Barada
The x-value of -7 shows up more than once in relation ...
B. X -7 -5 -7 2 Y 34 32 40 34
_____
When there is more than one y-value for an x-value, the relation is NOT a function.
B. X -7 -5 -7 2 Y 34 32 40 34
_____
When there is more than one y-value for an x-value, the relation is NOT a function.
