Question

Use the graph to answer the question.

Describe the continuity of the graphed function.

(1 point)
Responses

The function is continuous.
The function is continuous.

The function has a removable discontinuity at x = 3.
The function has a removable discontinuity at x = 3.

The function has a jump discontinuity at x = 3.
The function has a jump discontinuity at x = 3.

The function has an infinite discontinuity at x = 3.
The function has an infinite discontinuity at x = 3.

Answer 1

I can't see the graph you mean. Could you upload the image or describe what happens at x = 3 (left-hand y-value, right-hand y-value, and whether there's a filled dot or hole at x = 3)?

To help you decide, here are quick rules you can use:
- Continuous at x=3: left-hand limit = right-hand limit = function value f(3).
- Removable discontinuity at x=3: left-hand limit = right-hand limit but either f(3) is not defined or f(3) ≠ that common limit (a hole or a filled dot at a different height).
- Jump discontinuity at x=3: left-hand limit and right-hand limit both exist but are different.
- Infinite discontinuity at x=3: the function values blow up to ±∞ (vertical asymptote) as x approaches 3.

Send the graph or the values and I’ll pick the correct option.