Now, we can plot these ordered pairs on a coordinate plane and connect them to get the graph of p(x). Notice that p(x) is a transformation of f(x) and the graph of f(x)=|x| is V-shaped. Therefore, p(x) will also be a V-shaped graph.
Comparison
The function is in the form y=f(x-k), where k=4. Therefore, the graph of p is a horizontal translation 4 units right from the graph of f.
Domain and Range
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 0, and it will continue increasing indefinitely.
Range: 0 ≤ 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 < ∞
