Let's begin with creating a table of values of function u.
x
|x-1|+2
Simplify
u(x)
-3
| -3-1|+2
|-4|+2
6
-1
| -1-1|+2
|-2|+2
4
1
| 1-1|+2
|0|+2
2
3
| 3-1|+2
|2|+2
4
Now let's do the same with function v.
x
|-1/2x-1|+2
Simplify
v(x)
-4
|-1/2( -4)-1|+2
|1|+2
3
-2
|-1/2( -2)-1|+2
|0|+2
2
2
|-1/2( 2)-1|+2
|-2|+2
4
4
|-1/2( 4)-1|+2
|-3|+2
5
Finally, we can plot these ordered pairs on one coordinate plane.
Comparison
We can rewrite v(x) as u(- 12x), which is a horizontal stretch by a factor of 2 followed by a reflection in the y-axis. Note that the y-intercept is the same for both graphs.
