Question

this is the graph of function g.
select the x-values at which g has a jump discontinuity.
choose all answers that apply:
a x=0
b x=2
c x=6
d none of the above

Explanation:

Step1: Recall Jump Discontinuity

A jump discontinuity occurs when the left - hand limit and right - hand limit of a function at a point exist but are not equal, and the function may or may not be defined at that point.

Step2: Analyze \(x = 0\)

At \(x=0\), we have a situation where there are different types of discontinuities (not a jump). The function has a defined point, an open circle, etc., but the left - hand and right - hand behavior does not show a jump (the left - hand limit and right - hand limit do not have a non - equal finite jump here).

Step3: Analyze \(x = 2\)

At \(x = 2\), the function appears to be continuous (the graph passes through \(x = 2\) without a break or jump).

Step4: Analyze \(x=6\)

At \(x = 6\), we can see that the left - hand limit (from the left side of \(x = 6\)) and the right - hand limit (from the right side of \(x = 6\)) exist but are not equal. There is a jump between the left - hand part of the graph (the solid dot at \(y = 5\)) and the right - hand part (the open circle and the curve after \(x = 6\)). So \(x = 6\) has a jump discontinuity.

Answer:

C. \(x = 6\)