We will plot these ordered pairs on a coordinate plane and connect them to get the graph of t(x). Notice that t(x) is a transformation of the parent function f(x)=|x|, which is V-shaped. Therefore, t(x) will also be a V-shaped graph.
The domain of an absolute value function will usually be all real numbers, unless specific restrictions have been imposed upon the function.
Domain: -∞ < x < ∞
To find the range of an absolute value function, we need to think about where the vertex of the function 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 then it will continue decreasing indefinitely.
Range: -∞ < y ≤ 0
Comparing the Functions
To compare our graph to the graph of f(x)=|x|, let's draw them on one coordinate plane.
As we can see, the graph of t(x) is a vertical stretch of the graph of f(x) by a factor of 3 and a reflection in the x-axis.
