Final answer:
The graph of y = |4x| differs from the parent function y = |x| by having a steeper slope, which causes the V-shaped graph to be more narrow and rise or fall more rapidly.
Step-by-step explanation:
The question is about how the graph of the function y = |4x| differs from the graph of the absolute value parent function, which is y = |x|. When compared to the parent function y = |x|, the graph of y = |4x| will have a steeper slope due to the multiplier in front of x. This means that for every unit change in x, the value of y will change by four units, while in the case of the parent function it would only change by one unit.
The graph of y = |4x| is still a V-shaped graph characteristic of absolute value functions, but it is compressed horizontally by a factor of 1/4 compared to the graph of y = |x|. The V shape of the graph will look narrower because it rises and falls more quickly than the parent function. In other words, the y-values of the graph of y = |4x| increase or decrease more rapidly than those of the graph of y = |x| for the same x-values.