Question

Compare and contrast the following piecewise defined functions.

f(x) = {
A) -x + 2 for x < 2
B) 2 for 2 ≤ x < 5
C) x - 1 for x ≥ 5
D) None of the above

Answer 1

The given piecewise-defined functions are compared and contrasted based on their slopes, y-intercepts, and domains.

Step-by-step explanation:

The given piecewise defined functions are:
A) f(x) = -x + 2 for x < 2
B) f(x) = 2 for 2 ≤ x < 5
C) f(x) = x - 1 for x ≥ 5
To compare and contrast these functions, we can look at their slopes, y-intercepts, and domains.
A) The slope for the function A is -1, and the y-intercept is 2. The domain is x < 2.
B) The slope for the function B is 0 (since it is a horizontal line) and the y-intercept is 2. The domain is 2 ≤ x < 5.
C) The slope for the function C is 1, and the y-intercept is -1. The domain is x ≥ 5.
So, the functions differ in terms of their slopes, y-intercepts, and domains.