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Make a table of values to find points on the graph. Note that the graph of g(x) is a V-shaped graph.
Graph:
Comparison: See solution.
Let's graph g(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−1∣ | Simplify | g(x) |
---|---|---|---|
-3 | ∣-3−1∣ | ∣-4∣ | 4 |
-1 | ∣-1−1∣ | ∣-2∣ | 2 |
1 | ∣1−1∣ | ∣0∣ | 0 |
3 | ∣3−1∣ | ∣2∣ | 2 |
5 | ∣5−1∣ | ∣4∣ | 4 |
Now we can plot these ordered pairs on a coordinate plane and connect them to get the graph of g(x). Note that g(x) is a transformation of the graph of the parent function y=∣x∣, which is V-shaped. Therefore, g(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).
To compare our graph to the graph of f(x)=∣x−6∣, let's first draw this f(x). Note that this function is a horizontal translation 6 units right of the graph y=∣x∣.
Now when we have drawn function f(x), we can compare g(x) to it by drawing them on the same coordinate plane.
As we can see, the graph of g(x) is a horizontal translation 5 units left of the graph f(x).