The graph of h is a horizontal shrink of the graph of f by a factor of 12.
Practice makes perfect
First, let's use a table of values to find points on the graph of f(x)=- x+1.
x
- x+1
f(x)
0
-( 0)+1
1
2
-( 2)+1
-1
4
-( 4)+1
-3
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 h(x)=f(2x) differs from f(x).
x
f(x)
f(2x)
h(x)
0
1
-(2( 0))+1
1
2
-1
-(2( 2))+1
-3
4
-3
-(2( 4))+1
-7
If we plot these points on the same coordinate plane as f(x), we can see that our points have been shrunk to half as far away from the y-axis as they were before.
Therefore, the graph of h is a horizontal shrink of the graph of f by a factor of 12.
