Question

The function f(x) = |x - 1| is continuous:

a) at x >= 0 only
b) discontinuous at x = 1
c) continuous everywhere
d) undefined at x = 1

Answer 1

The function f(x) = |x - 1| is continuous everywhere on its domain, including at x = 1 and beyond, showcasing no discontinuities or points of undefined behavior.

Step-by-step explanation:

The function f(x) = |x - 1| is an example of an absolute value function, which is continuous everywhere on its domain. The question asks whether this function is continuous only at x ≥ 0, discontinuous at x = 1, continuous everywhere, or undefined at x = 1. By definition, an absolute value function is continuous at all points in its domain because there are no breaks, holes, or jumps in the graph of the function. Specifically, |x - 1| has a V-shaped graph that pivots at x = 1, and is continuous through this point and all others.

Therefore, the correct answer to this question is (c) the function is continuous everywhere on its domain, including at and beyond x = 1.