Question

Given `h (x) = -e^x`, how do you describe the transformation?

Answer 1

`h(x)` is a reflection over the `x`-axis of `f(x)=e^x`

Explanation:

If there is a parent function `f(x)`, `-f(x)` represents a reflection over the `x`-axis, while `f(-x)` represents a reflection over the `y`-axis.

In this case, the parent function is `f(x)=e^x`.
`h(x)=-e^x=-f(x)`
Thus, `h(x)` is a reflection over the `x`-axis of `f(x)`.

We can verify this by graphing the two functions.

This is the graph of `f(x)`:
graph{e^x [-10, 10, -5, 5]}

This is the graph `h(x)`:
graph{-(e)^x [-10, 10, -5, 5]}

This is clearly a reflection over the `x`-axis.