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

##### 1 Answer
Apr 25, 2017

$g \left(x\right) = f \left(- \left(x - 3\right)\right)$

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.

$f \left(x\right) = {10}^{x}$

$g \left(x\right) = {10}^{- x + 3}$

so it follows that

$g \left(x\right) = f \left(- x + 3\right)$

We should know that $f \left(- x\right)$ is a reflection of $f \left(x\right)$ and $f \left(x - a\right)$ is a translation of $f \left(x\right)$ 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 $- \left(x - 3\right)$ it should help you to realise the shift.
graph{10^(-x+3) [-1.077, 6.523, -0.44, 3.36]}