Make a table of values to find points on the graph. Notice that the graph of h(x) is a V-shaped graph.
Graph:
Comparison: See solution.
Practice makes perfect
Let's graph h(x) first and then we can compare it to the graph of f(x).
Graphing h(x)
To graph the function without going through the entire process of transforming the parent function, we can make a table of values. Then we only need to plot the ordered pairs that we find.
x
|x-6|+2
Simplify
h(x)=|x-6|+2
0
| 0-6|+2
|-6|+2
8
2
| 2-6|+2
|-4|+2
6
4
| 4-6|+2
|-2|+2
4
6
| 6-6|+2
|0|+2
2
8
| 8-6|+2
|2|+2
4
10
| 10-6|+2
|4|+2
6
12
| 12-6|+2
|6|+2
8
Now we can plot these ordered pairs on a coordinate plane and connect them to get the graph of h(x). Notice that h(x) is a transformation of the graph of the parent function y=|x|, which is V-shaped. Therefore, h(x) will also be a V-shaped graph.
Now that we have graphed our function, we can move on to comparing it to f(x).
Comparing the Functions
To compare the graph of h(x) to the graph of f(x)=|x-6|, let's first draw this function. Notice that f(x) is a horizontal translation 6 units to the right of the graph of the parent function y=|x|.
Now that we have drawn f(x), we can compare h(x) to it.
As we can see, the graph of h(x) is a vertical translation 2 units up from the graph of f(x).
