Is absolute value continuous?
Understand the Problem
The question is asking whether the absolute value function is continuous. Understanding continuity involves knowing that a function is continuous if there are no breaks, jumps, or holes in its graph. For the absolute value function, we would need to examine its behavior particularly around the point where the function changes from positive to negative values.
Answer
The absolute value function is continuous everywhere.
The absolute value function is continuous everywhere.
Answer for screen readers
The absolute value function is continuous everywhere.
More Information
The absolute value function, f(x) = |x|, is continuous everywhere. However, it is only differentiable everywhere except at x = 0.
Tips
A common mistake is to think that the piecewise nature of the absolute value function implies discontinuity. Continuity simply means that the function does not have any jumps or breaks.
Sources
- Absolute value function is continuous everywhere - Wikipedia - en.wikipedia.org
- Absolute Value Function is Continuous - ProofWiki - proofwiki.org
- Why absolute-value function is not a continuous function - Math Stack Exchange - math.stackexchange.com
