The graph of r is a horizontal stretch of the graph of f by a factor of 2.
Practice makes perfect
First, let's use a table of values to find points on the graph of f(x)=- 2x-4.
x
- 2x-4
f(x)
0
- 2( 0)-4
-4
2
-2( 2)-4
-8
4
-2( 4)-4
-12
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)=f( 12x) differs from f(x).
x
f(x)
f(1/2x)
r(x)
0
-4
-2(1/2( 0))-4
-4
2
-8
-2(1/2( 2))-4
-6
4
-12
-2(1/2( 4))-4
-8
If we plot these points on the same coordinate plane as f(x), we can see that our points have been stretched twice as far from the y-axis as they were before.
Therefore the graph of r is a horizontal stretch of the graph of f by a factor of 2.
