# How do you use transformations to describe the relationship between the graph of f(x) = x and the graph of h(x) = -1/15x + 12?

Jul 19, 2018

We have three transformations that we'd normally use:
Stretching (or scaling), shifting, and flipping.

If we start with a straight line with slope one, in order to get the final equation, we need to flip it (because of the -), scale it by a factor of 1/15, then shift it up by a factor of 12.

To check your understanding, you may want to see how you'd get back from $h \left(x\right)$ to $f \left(x\right)$. I'd say that you do this:
Shift down by 12, scale by a factor of 15, then flip.

Jul 19, 2018

#### Explanation:

Given: f(x) = x; " "h(x) = -1/15x + 12

The parent function $f \left(x\right)$ is a line that has a slope $m = 1$ and goes through the $y$-intercept of $\left(0 , 0\right)$

$h \left(x\right)$ has been reflected about the $x$-axis (due to the negative sign), horizontally stretched by $\frac{1}{15}$ and shifted vertically up by $12$.

$h \left(x\right) : y \text{-intercept of "(0, 12), "and has a slope } m = - \frac{1}{15}$.

Graph of the two functions:

graph{(y - x)(y +1/15x - 12)=0 [-40, 40, -20, 20]}