Question

Is `y=x^2 + 3x - 15` a function?

Answer 1

Yes, it is (in the usual sense that `y` is a function of `x`).

For any value of `x`, the expression gives only one (never two or more) values for `y`.

Here is the graph on `y=x^2+3x-15`. As you can see, it passes the vertical line test.

graph{y=x^2+3x-15 [-33.55, 31.4, -23.03, 9.46]}

(There are many times that 2 values of `x` give the same value of `y`, but that is ok for a function.)