Now, we can plot these ordered pairs on a coordinate plane and connect them to get the graph of q(x). Notice that q(x) is a transformation of f(x) and the graph of f(x)=|x| is V-shaped. Therefore, q(x) will also be a V-shaped graph.
Comparison
We can note that r is in the form y=- af(x). Recall that the graph of y=- af(x) is a vertical stretch or shrink and a reflection in the x-axis. Because a= 14, the graph of r is a vertical shrink from the graph of f by a factor of 14 and a reflection in the x-axis.
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 maximum of the given function is 0, and it will continue decreasing indefinitely.
Range: - ∞ < y < 0
The domain of an absolute value function will usually be all real numbers, unless specific restrictions have been imposed upon the function.
Domain: -∞ < x < ∞
