The graph of g is a vertical stretch of the graph of f by a factor of 6.
Practice makes perfect
First, let's use a table of values to find points on the graph of f(x)=x-6.
x
x-6
f(x)
0
( 0)-6
-6
2
( 2)-6
-4
4
( 4)-6
-2
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 g(x)=6f(x) differs from f(x).
x
f(x)
6f(x)
g(x)
0
-6
6( -6)
-36
2
-4
6( -4)
-24
4
-2
6( -2)
-12
If we plot these points on the same coordinate plane as f(x), we can see that our points have been stretched to six times as far from the x-axis as they were before.
Therefore, the graph of g is a vertical stretch of the graph of f by a factor of 6.
