Question

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`?

Answer 1

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(x)` to `f(x)`. I'd say that you do this:
Shift down by 12, scale by a factor of 15, then flip.

Answer 2

See answer below

Explanation:

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

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

`h(x)` has been reflected about the `x`-axis (due to the negative sign), horizontally stretched by `1/15` and shifted vertically up by `12`.

`h(x): y"-intercept of "(0, 12), "and has a slope " m = -1/15`.

Graph of the two functions:

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