Question

which statement correctly explains whether the equation $y = x^2 - 2$ represents a function?
○ it is not a function because $y = 2$ when $x = 2$ or $x = -2$.
○ it is not a function because there are no $y$-values less than $-2$.
○ it is a function because there is only one $y$-value for each $x$-value.
○ it is a function because there is only one $x$-value for each $y$-value.

Explanation:

A function is defined such that every input (x-value) has exactly one output (y-value). For the equation \(y = x^2 - 2\), substituting any single x-value will result in only one corresponding y-value. The fact that multiple x-values can lead to the same y-value does not violate the function definition, and the range restriction (y ≥ -2) also does not affect its status as a function.

Answer:

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