Question

What value(s) of x in the relation below would

create a set of ordered pairs that is not a function?
Justify your answer.
{(0, 5) (1, 5) (2, 6) (x, 7)}

Answer 1

3 Answers: x = 0, x = 1, or x = 2

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Step-by-step explanation:

The relation

{(0, 5) (1, 5) (2, 6) (x, 7)}

has points with x coordinates of: 0, 1, 2, and x.

If we repeated any of the x values listed so far, then we will not have a function.

So if we had the points (0,5) and (0,7), then the input x = 0 leads to multiple outputs. A function is only possible when any input x leads to exactly one output y.

This means that if x = 0, 1, or 2, then we won't have a function.

Side note: The y values can repeat, but if they do, then we won't have a one-to-one function. In this case, y = 5 repeats, so this function is not one-to-one (assuming x is not 0, not 1, and not 2).