7. Graphing Absolute Value Functions
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Recall the general forms for translations.
Is Our Friend Correct? No
Explanation: See solution.
x | ∣x∣ | y=∣x∣ |
---|---|---|
-2 | ∣-2∣ | 2 |
-1 | ∣-1∣ | 1 |
0 | ∣0∣ | 0 |
1 | ∣1∣ | 1 |
2 | ∣2∣ | 2 |
Let's now make a table of values for y=∣x+p∣. We will arbitrarily let p=2, resulting in the function y=∣x+2∣.
x | ∣x+2∣ | y=∣x+2∣ |
---|---|---|
-2 | ∣-2+2∣ | 0 |
-1 | ∣-1+2∣ | 1 |
0 | ∣0+2∣ | 2 |
1 | ∣1+2∣ | 3 |
2 | ∣2+2∣ | 4 |
Finally let's make a table for y=∣x+p∣, with p=-2. The resulting function is y=∣x−2∣.
x | ∣x−2∣ | y=∣x−2∣ |
---|---|---|
-2 | ∣-2−2∣ | 4 |
-1 | ∣-1−2∣ | 3 |
0 | ∣0−2∣ | 2 |
1 | ∣1−2∣ | 1 |
2 | ∣2−2∣ | 0 |
We can plot and connect the obtained points in the same coordinate plane. Keep in mind that the graph of an absolute value function has a V
shape.
Though it may seem counterintuitive, the graph of y=∣x+2∣ is a negative horizontal translation of the graph of y=∣x∣ by 2 units. Conversely, the graph of y=∣x−2∣ is a positive horizontal translation of the graph of y=∣x∣ by 2 units.