The graph of h is a horizontal shrink of the graph of f by a factor of 15.
Practice makes perfect
First, let's use a table of values to find points on the graph of f(x)=-2 x-2.
x
-2 x-2
f(x)
0
-2( 0)-2
-2
5
-2( 5)-2
-12
10
-2( 10)-2
-22
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)=f(5x) differs from f(x).
x
-2 x - 2
f(x)
f(5x)
h(x)
0
-2( 0) - 2
-2
-2(5( 0))-2
-2
1
-2( 1) - 2
-4
-2(5( 1))-2
-12
2
-2( 2) - 2
-6
-2(5( 2))-2
-22
If we plot these points on the same coordinate plane as f(x), we can see that our points have been shrunk to be one fifth as far away from the y-axis as they were before.
Therefore, the graph of h is a horizontal shrink of the graph of f by a factor of 15.
