The graph of r is a vertical stretch of the graph of f by a factor of 4.
Practice makes perfect
First, let's use a table of values to find points on the graph of f(x)=- 14x-2.
x
-1/4x-2
f(x)
0
-1/4( 0)-2
-2
4
-1/4( 4)-2
-3
8
-1/4( 8)-2
-4
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 r(x)=4f(x) differs from f(x).
x
f(x)
4f(x)
r(x)
0
- 2
4( - 2)
- 8
4
- 3
4( - 3)
-12
8
- 4
4( -4)
-16
If we plot these points on the same coordinate plane as f(x), we can see that our points have been stretched four times as far from the x-axis as they were before.
Therefore, the graph of r is a vertical stretch of the graph of f by a factor of 4.
