Final answer:
Changing the values of m in the function f(x) = mx alters the slope of the graph, while modifying the value of a in the graph of g(x) = a |x| affects the steepness of the V-shaped graph.
Step-by-step explanation:
When altering the values of m and a in the functions f(x) = mx and g(x) = a |x| respectively, we are effectively changing the slopes and shapes of these graphs compared to their parent functions. The value of m determines the steepness or gradient of the line in the function f(x). If m is positive, the line slopes upward to the right; if m is negative, it slopes downward. For the function g(x), the value of a affects how steep the V-shaped graph will be. A larger absolute value of a will make the graph steeper, while a smaller absolute value will make it wider.
For instance, the parent function of f(x) is simply y = x which has a gradient of 1. Altering the value of m will change the slope. Similarly, the parent function of g(x) is y = |x|, and changing a will affect the sharpness of the V shape. Both functions have the y-intercept at the origin (0,0), but altering m or a does not change this intercept, only the shape and steepness of the graph.