Final answer:
The graph of y = 3|x| will be steeper than the graph of y = |x|, with a slope three times as steep, maintaining its V-shape but with y-values that increase or decrease three times as quickly.
Step-by-step explanation:
The graph of y = 3|x| compared to the Absolute Value parent function y = |x| will be steeper. The coefficient of 3 in y = 3|x| signifies that for every unit the x-value increases, the y-value will rise by 3 units instead of 1. This is because the slope is effectively multiplied by 3. The V-shape of the absolute value function will remain, but the arms of the graph will be three times as steep as those of the parent function. The graph will still pass through the origin (0,0) since the absolute value function's graph always passes through the origin, but the y-values will increase (or decrease, when x is negative) at a quicker rate.