Answer: Jump discontinuity.
- A Removable
- B Jump discontinuity
- C No discontinuity
- D Infinite discontinuity
Correct answer: B. Jump discontinuity
Explanation: When the left-hand limit and right-hand limit exist but are unequal, the function has a jump (first kind) discontinuity.
f(x)=|x| is perfectly continuous at x=0 (no break, no jump), but the curve has a sharp corner there: approaching from the left gives slope -1 and from the right gives slope +1 - since these one-sided derivatives disagree, the function is not differentiable at that point.
Concept context
When a function has no breaks (continuity) and when it has a well-defined slope (differentiability), plus rules for differentiating implicit, inverse trig, exponential, log, and parametric functions.