Let's begin with creating a table of values of function w.
x
|x-3|+4
Simplify
w(x)
-2
| -2-3|+4
|-5|+4
9
0
| 0-3|+4
|-3|+4
7
2
| 2-3|+4
|-1|+4
5
4
| 4-3|+4
|1|+4
5
Now we will do the same with function y.
x
|5x-3|+4
Simplify
y(x)
-1
|5( -1)-3|+4
|-8|+4
12
3/5
|5( 3/5)-3|+4
|0|+4
4
1
|5( 1)-3|+4
|2|+4
6
2
|5( 2)-3|+4
|7|+4
11
Finally, we can plot these ordered pairs on one coordinate plane.
Comparison
We can rewrite y(x) as w(5x), which is a horizontal shrink by a factor of 15. It is being shrunk closer the y-axis. Note that when the x-values of w are five times the x-values of y, the y-values stay the same.
