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#?

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

Jul 19, 2018

Answer:

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]}