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Make a table of values to find points on the graph. Note that the graph of r(x) is a V-shaped graph.
Graph:
Domain: All real numbers
Range: y≥5
Comparison: See solution.
Let's graph r(x) first and then we can compare it to the graph of f(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∣+5 | Simplify | r(x)=∣x∣+5 |
---|---|---|---|
-5 | ∣-5∣+5 | 5+5 | 10 |
-3 | ∣-3∣+5 | 3+5 | 8 |
-1 | ∣-1∣+5 | 1+5 | 6 |
0 | ∣0∣+5 | 0+5 | 5 |
1 | ∣1∣+5 | 1+5 | 6 |
3 | ∣3∣+5 | 3+5 | 8 |
5 | ∣5∣+5 | 5+5 | 10 |
Now we can plot these ordered pairs on a coordinate plane and connect them to get the graph of r(x). Note that r(x) is a transformation of f(x) and the graph of f(x)=∣x∣ is V-shaped. Therefore, r(x) will also be a V-shaped graph.
To compare our graph to the graph f(x)=∣x∣, let's draw them on one coordinate plane.
As we can see, the graph of r(x) is a vertical translation 5 units up of the graph f(x).