Question

How do you use the graph of `f(x)=10^x` to describe the transformation of `g(x)=10^(-x+3)`?

Answer 1

`g(x) = f(-(x-3))`

A translation by 3 in the x direction followed by a reflection.

Explanation:

I hate these combined transformation type questions. What you need to look at here is the argument for the function.

`f(x)=10^x`

`g(x)=10^(-x+3)`

so it follows that

`g(x)=f(-x+3)`

We should know that `f(-x)` is a reflection of `f(x)` and `f(x - a)` is a translation of `f(x)` by `a` in the x direction (sorry, can't seem to write vectors on here). The difficult thing to get your head around is the order in which the transformations are applied.

By writing `-x+3` as `-(x-3)` it should help you to realise the shift.
graph{10^(-x+3) [-1.077, 6.523, -0.44, 3.36]}