Question

consider the function graphed below. at what x - values does the function appear to not be continuous? x = at what x - values does the function appear to not be differentiable? x = (enter none if there are no x - values that apply; enter x - values as a comma - separated list, e.g., 1,3,5)

Explanation:

Step1: Recall continuity condition

A function is dis - continuous at a point if there is a break, jump or hole. Visually inspect the graph.

Step2: Identify dis - continuity points

There is a jump at \(x = 1\), so the function is not continuous at \(x=1\).

Step3: Recall differentiability condition

A function is not differentiable at a point if there is a sharp corner, a vertical tangent or a discontinuity.

Step4: Identify non - differentiable points

There is a sharp corner at \(x = 4\) and a discontinuity at \(x = 1\). So the function is not differentiable at \(x = 1,4\).

Answer:

At what \(x\) - values does the function appear to not be continuous? \(x = 1\)
At what \(x\) - values does the function appear to not be differentiable? \(x = 1,4\)