Question

Is `f(x)=(x^2 - 3x - 4)/(x^2 + 1)` a function?

Answer 1

Yes! When you plug in an x value for this function, you get a unique y-value.

A graph is only a function if each input (x-value) has no more than 1 output (y-value). This doesn't mean that each y-value only corresponds to 1 x-value. Usually that's NOT the case.

I feel like this answer is too simple so here's a graph of the function you named. graph{(x^2 - 3x - 4) / (x^2 + 1) [-12.87, 13.86, -7.24, 6.13]} Functions are also notable for passing the "vertical line" test. If you place a vertical line on any point on a graph, and that vertical line NEVER crosses the graph more than once, then the graph is a function. This function obviously passes!