Answer:
The graphs of the three functions A, B, and C are all different because they have different coefficients and signs in front of the absolute value function. Here is an explanation of the differences between the graphs:
A. f(x) = - |x|
This function is the opposite of the absolute value function. It takes the absolute value of x, and then multiplies the result by -1. This means that for any value of x, the output of the function is the negative of the absolute value of x. The graph of this function is a "V" shape that opens downward, with the vertex at the origin (0,0).
B. f(x) = 3/4 |x|
This function is a scaled version of the absolute value function. It takes the absolute value of x, and then multiplies the result by 3/4. This means that for any value of x, the output of the function is 3/4 of the absolute value of x. The graph of this function is a "V" shape that opens upward, with the vertex at the origin (0,0), and the slope of the arms of the "V" being less steep than the slope of the arms for the absolute value function.
C. f(x) = 4 |x|
This function is a scaled version of the absolute value function as well, but it has a different scale factor. It takes the absolute value of x, and then multiplies the result by 4. This means that for any value of x, the output of the function is 4 times the absolute value of x. The graph of this function is a "V" shape that opens upward, with the vertex at the origin (0,0), and the slope of the arms of the "V" being steeper than the slope of the arms for the absolute value function.
In summary, the graphs of these three functions are all "V" shapes, but they differ in terms of their orientation, their vertex location, and the steepness of the arms of the "V".