Make a table of values and remember that the graph of r(x) is a V-shaped graph.
Graph:
Description: The graph of r is a vertical stretch of the graph of f by a factor 2 and a reflection in the x-axis. Domain: All real numbers. Range: y≤0
Practice makes perfect
Let's graph r(x) first, and then we can compare it to the graph of f(x).
Now we can plot these ordered pairs on a coordinate plane and connect them to get the graph of r(x). Notice that r(x) is a transformation of f(x) and the graph of f(x)=|x| is V-shaped. Therefore, r(x) will also be a V-shaped graph.
To find the domain and range of an absolute value function, we need to consider the location of the vertex. Because this type of function always has 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 is usually all real numbers, unless specific restrictions have been imposed upon the function.
Domain: all real numbers
Comparing With the Graph of f(x)=|x|
To compare our graph with the graph f(x)=|x|, let's draw them on the same coordinate plan.
We can see the graph of r(x) is a vertical stretch of the graph f(x) by a factor of 2 followed by a reflection in the x-axis.
