at what points is f(x) continuous? (choose all that apply.)\nx=-3\nx=0\nx=1\nx=2\nx=4\nview hint for…

Explanation:

Step1: Recall continuity criteria

A function is continuous at a point if the limit as x approaches the point from the left equals the limit as x approaches the point from the right and equals the function - value at that point.

Step2: Analyze x = - 3

Looking at the graph, the function has no breaks, jumps, or holes at x=-3. The left - hand limit, right - hand limit, and the function value are the same. So it is continuous at x = - 3.

Step3: Analyze x = 0

There is a vertical asymptote at x = 0. The function approaches infinity or negative infinity as x approaches 0, so it is not continuous at x = 0.

Step4: Analyze x = 1

There is a break in the graph at x = 1. The left - hand limit and right - hand limit do not match up, so it is not continuous at x = 1.

Step5: Analyze x = 2

There is a hole in the graph at x = 2. The limit exists but the function is not defined at the exact point x = 2 in a proper continuous way, so it is not continuous at x = 2.

Step6: Analyze x = 4

There is a jump in the graph at x = 4. The left - hand limit and right - hand limit are different, so it is not continuous at x = 4.

Answer:

x=-3