Learn how to determine if a function is continuous and differentiable

The video tutorial explains how to check the continuity of a graph, focusing on identifying holes in piecewise functions. It highlights that a function with a hole is not continuous and therefore not differentiable. The tutorial uses graphing examples to illustrate these concepts, emphasizing the relationship between continuity, limits, and differentiability.

What is the first step in checking the continuity of a graph?

• Calculating the derivative

• Plotting the graph

• Identifying the domain of the function

• Finding the range of the function

What happens at a point where a graph has a hole?

• The function is continuous

• The function is differentiable

• The function is not continuous

• The function is undefined

How does a piecewise function affect continuity?

• It always makes the function continuous

• It can create discontinuities

• It has no effect on continuity

• It makes the function differentiable

Why can't a function with a discontinuity be differentiable?

• Because it is piecewise

• Because it is continuous

• Because it has a derivative

• Because it lacks a smooth curve

What is the relationship between continuity and differentiability?

• A function must be continuous to be differentiable

• Continuity and differentiability are unrelated

• A function can be differentiable without being continuous

• Differentiability ensures continuity