Question

What does the transformation f(x) --> -f(x) do to the graph of f(x)

Answer 1

Answer: D) Reflect over x-axis

=======================================================

Explanation:

When we do this type of reflection, a point like (1,2) moves to (1,-2).

As another example, something like (5,-7) moves to (5,7)

The x coordinate stays the same but the y coordinate flips in sign from positive to negative, or vice versa.

We can say that $(x,y) \to (x,-y)$ as a general way to represent the transformation. Note how y = f(x), so when we make f(x) negative, then we're really making y negative.

If we apply this transformation to every point on f(x), then it will flip the f(x) curve over the horizontal x axis.

There's an example below in the graph. The point A(2,8) moves to B(2,-8) after applying that reflection rule.