The graph of r is a horizontal stretch of the graph of f by a factor of 3.
Practice makes perfect
First, let's use a table of values to find points on the graph of f(x)=3x+5.
x
3x+5
f(x)
0
3( 0)+5
5
2
3( 2)+5
11
4
3( 4)+5
17
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( 13x) differs from f(x).
x
3x + 5
f(x)
f(1/3x)
r(x)
0
3( 0) + 5
5
3(1/3( 0))+5
5
6
3( 6) + 5
23
3(1/3( 6))+5
11
12
3( 12) + 5
41
3(1/3( 12))+5
17
If we plot these points on the same coordinate plane as f(x), we can see that our points have been stretched three times 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 3.
