Final answer:
The function f(x) = 40|x - 1.25| has a V-shaped graph with a vertex at the point (1.25, 0) and is decreasing for x < 1.25. The graph is linear with two different slopes that meet at the vertex, which is distinct from horizontal lines or quadratic functions.
Step-by-step explanation:
Understanding the Function f(x) = 40|x - 1.25|
The function f(x) = 40|x - 1.25| represents a V-shaped graph which is symmetrical about the line x = 1.25. This point is the vertex of the absolute value function and occurs at the minimum value of the function. For values of x less than 1.25, the function is decreasing because as x gets closer to 1.25 from the left, the absolute value of (x - 1.25) gets smaller, thus making the entire function value smaller. Conversely, for values of x greater than 1.25, the function is increasing because as x moves away from 1.25 to the right, the positive difference (x - 1.25) gets larger, and hence the function's value increases proportionally.
At the vertex (1.25, 0), the function achieves its minimum value since the absolute value of (1.25 - 1.25) is zero, and any factor multiplied by zero is zero. The function's graph is not a horizontal line, an exponential decay, or a parabolic curve, but rather a linear graph with two different slopes meeting at the vertex.
Regarding other examples, for a horizontal line equation like f(x) = 20, the function value doesn't change regardless of x, within the domain 0 ≤ x ≤ 20. This is quite different from the original function given, where the value of f(x) changes with x. Moreover, for a function with a positive value and a positive slope that decreases as x increases, such as a quadratic function y = x², it is initially increasing at a decreasing rate for positive x values - another concept distinct from the behavior of the absolute value function we are focusing on.