Below are the functions of y = |x| and y = |x| – 5. How are the functions related?
Two absolute value graphs are shown.
The first function, y = |x|, represents the absolute value of x. It is a V-shaped graph that opens upward, symmetric about the y-axis. This function will have a y-value of 0 when x=0.
The second function, y = |x| – 5, is obtained by shifting the graph of y = |x| downward by 5 units. It is a V-shaped graph, symmetric about the y-axis, but with a vertical shift downwards by 5 units compared to the original function.
Therefore, the two functions are related by a vertical shift downward of 5 units.