Question

When you multiply a function by –1, what is the effect on its graph?

A.
The graph flips over the y-axis.

B.
The graph flips over the line y = x.

C.
The graph flips over the x-axis.

Answer 1

Answer: C) The graph flips over the x axis.

This is because we're multiplying the y outputs by -1, to make them flip in sign from positive to negative (or vice versa).

Let's say the point (1,2) is on the f(x) curve. Multiplying y = f(x) by -1 will make the point turn into (1,-2). Apply this logic to every point on the f(x) curve and we end up with f(x) reflected over the horizontal x axis.

The notation we could write is either g(x) = -1*f(x) or g(x) = -f(x).