The graph of r is a vertical 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 graph of f(x)= 23x+1.
x
2/3x+1
f(x)
0
2/3( 0)+1
1
3
2/3( 3)+1
3
6
2/3( 6)+1
5
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)=3f(x) differs from f(x).
x
f(x)
3f(x)
r(x)
0
1
3( 1)
3
3
3
3( 3)
9
6
5
3( 5)
15
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 x-axis as they were before.
Therefore, the graph of r is a vertical stretch of the graph of f by a factor of 3.
