Question

which statement correctly explains whether the equation $y = x^2 - 2$ represents a function?

1. it is not a function because there are no y-values less than -2.
2. it is a function because there is only one y-value for each x-value
3. it is a function because there is only one x-value for each y-value.
4. it is not a function because $y=2$ when $x=2$ or $x=-2$.

Explanation:

A function is defined such that for every input (x-value), there is exactly one corresponding output (y-value). For the equation $y = x^2 - 2$, substituting any single x-value will result in only one y-value. The other options are incorrect: the range of y-values being no less than -2 does not determine if it is a function; a function does not require one x-value per y-value; and having the same y-value for different x-values is allowed in a function.

Answer:

B. It is a function because there is only one y-value for each x-value