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Let's graph m(x). 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|+6 | Simplify | m(x) |
|---|---|---|---|
| -1 | | -1|+6 | 1+6 | 7 |
| 0 | | 0|+6 | 0+6 | 6 |
| 1 | | 1|+6 | 1+6 | 7 |
The function is in the form y=f(x)+k, where k=6. Therefore, the graph of m is a vertical translation 6 units up from the graph of f.
To find the domain and range of an absolute value function, we need to think about where the vertex is located. Because this type of function will always have the same basic V-shape, the y-value of the vertex is the minimum or maximum of the range. The minimum of the given function is 6, and it will continue increasing indefinitely. Range: 6 ≤ y < ∞ The domain of an absolute value function will usually be all real numbers, unless specific restrictions have been imposed upon the function. Domain: -∞ < x < ∞
