Answer:
(b) When a vertical line intersects the graph of a relation more than once, it indicates that for that input there is more than one output, which means the relation is not a function.
Explanation:
You want to know why the vertical line test tells us whether the graph of a relation represents a function.
Function
A relation maps a set of inputs to a set of outputs. A function maps a set of unique inputs to a set of outputs. That is, the elements of the input set of a function are not repeated, but appear only once.
On the graph of a relation, the input values are mapped to the horizontal coordinate(s) of the point(s) on the graph. If the relation has repeated input values, then those points will have the same x-coordinate on a graph, and will lie on a vertical line. So, we can conclude ...
When a vertical line intersects the graph of a relation more than once, it indicates that for that input there is more than one output, which means the relation is not a function.
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Additional comment
You can narrow the choices by considering their vocabulary. The question asks about the graph of a relation. Choices A and D talk about the graph of a function, so can be rejected immediately.
The subject of the question is a vertical line. As you know, a vertical line is of the form x = constant, where an (x, y) ordered pair is an (input, output) pair of a relation. Thus a vertical line will be referring to one input value that is a constant. Choice C talks about "more than one input", which has no relationship to a vertical line. Hence the only choice that makes any sense in the context of the question is B.
A lot of multiple choice questions can be answered appropriately just by considering the way the question and answers are worded.
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