Question

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

Answer 1

It is a reflection across the y-axis of `f(x)=e^x`

Explanation:

I'm going to assume you mean the transformation from the parent function `f(x) = e^x`.

Let's think about how to get `e^-x` from `f(x)`:

You would have to plug in `-x` instead of `x`, giving `f(-x)=e^-x`

Therefore we can say that:

`h(x) = f(-x)`

What does this mean as far as transformation on a graph? Well...

The point `(2, e^2)` on `f(x)` will correspond to the point `(-2, e^2)` on `h(x)`.

In fact, plugging in any value into f(x) and then plugging in the negative of that value to h(x) will give the same answer.

This basically means that the x-values of `f(x)` become the negative of what they were originally.

Graphically, this means the graph of `f(x)` is reflected across the y-axis to get `h(x)`.

You can see this below: `e^x` and `e^-x` are graphed together to show how `e^-x` is a reflection of `e^x`.

`color(white)"XXXXXXXXXXXXXX-"e^-x color(white)"XXXXX"e^x`
`color(white)"XXXXXXXXXXXXXX-"darr color(white)"XXXXX"darr`
graph{(y-e^x)(y-e^-x)=0 [-10.16, 9.84, -3.4, 6.6]}