Sketch both graphs on the same coordinate plane. Observe their similarities and differences.
See solution.
Practice makes perfect
First let's draw the graphs of y=|x|-4 and y=|x-4| on the same coordinate plane. To draw the first function, consider the following general equation, where k is a real number.
y=|x|+ k
The graph of this equation is a vertical translation of y=|x| by k units. In this case, the value of k is - 4. Therefore, the graph of y=|x|-4 is the graph of y=|x| translated 4 units down. To draw the second function, consider the following general equation where h is a positive number.
y=|x- h|
The graph of this equation is a horizontal translation of y=|x| by h units to the right. In this case, the value of h is 4. Therefore, the graph of y=|x-4| is the graph of y=|x| translated 4 units to the right.
Now we can compare them.
Similarities
Both graphs have the same V-shape.
The graphs overlap when x≥ 4 and are parallel when y<0.
