Function values can be positive or negative, and they can increase or decrease as the input increases.

Can function values ever be negative?

It definitely can, say f(x)=−1 for every possible x. The average of f in any interval is −1.

What happens when a function is negative?

To keep straight what this transformation does, remember that f (x) is the exact same thing as y. So, by putting a "minus" on everything, you're changing all the positive (above-axis) y-values to negative (below-axis) y-values, and vice versa. (Any points on the x-axis stay right where they are.