The graph of h is a vertical shrink of the graph of f by a factor of 16.
Practice makes perfect
First, let's use a table of values to find points on the graph of f(x)=3x-12.
x
3x-12
f(x)
0
3( 0)-12
-12
2
3( 2)-12
-6
4
3( 4)-12
0
We can plot these points and connect them with a straight line to have the graph of f(x).
Now, let's look at how the function h(x)= 16f(x) differs from f(x).
x
f(x)
16f(x)
h(x)
0
-12
1/6( -12)
-2
2
-6
1/6( -6)
-1
4
0
1/6( 0)
0
If we plot these points on the same coordinate plane as f(x), we can see that our points have been shrunk six times as close to the x-axis as they were before.
Therefore, the graph of h is a vertical shrink of the graph of f by a factor of 16.
