Now we can plot these ordered pairs on a coordinate plane and connect them to draw the graph of b(x). Note that b(x) is a transformation of the graph of the parent function y=|x|, which is V-shaped. Therefore, b(x) will also be a V-shaped graph.
Now that we have graphed our function, we can move on to comparing it to function f(x).
Comparing the Functions
To compare our graph to the graph of f(x)=|x+3|-2, let's first draw this function. We will start with making a table of values, just like we did with function y(x).
x
|x+3|-2
Simplify
f(x)
-7
| -7+3|-2
|-4|-2
2
-5
| -5+3|-2
|-2|-2
0
-3
| -3+3|-2
|0|-2
-2
-1
| -1+3|-2
|2|-2
0
1
| 1+3|-2
|4|-2
2
Now we can use the obtained ordered pairs to graph the function of f(x).
Now when we have drawn the graph of f(x), we can compare b(x) to it by drawing both graphs on the same coordinate plane.
As we can see, the graph of b(x) is a vertical translation 5 units up of the graph f(x).
