Understanding Continuity and Discontinuities

What is a point discontinuity also known as?

• Infinite discontinuity

• Non-removable discontinuity

• Jump discontinuity

• Removable discontinuity

Which type of discontinuity involves a sudden change from one piece of the graph to another?

• Jump discontinuity

• Infinite discontinuity

• Removable discontinuity

• Point discontinuity

What is another name for an infinite discontinuity?

• Point discontinuity

• Vertical asymptote

• Horizontal asymptote

• Jump discontinuity

In the given graph example, what type of discontinuity is found at x = 1?

• Point discontinuity

• Jump discontinuity

• Removable discontinuity

• Infinite discontinuity

What type of discontinuity is present at x = 2 in the graph example?

• Infinite discontinuity

• Point discontinuity

• Removable discontinuity

• Jump discontinuity

When does a rational function typically have a discontinuity?

• When the function is undefined

• When both numerator and denominator are zero

• When the numerator is zero

• When the denominator is zero

What happens when a factor in a rational function reduces to zero?

• It creates a jump discontinuity

• It creates an infinite discontinuity

• It creates a point discontinuity

• It creates a removable discontinuity

Which condition is NOT required for a function to be continuous at a point?

• The function must be differentiable at that point

• The limit must equal the function's value at that point

• The limit must exist as it approaches the point

• The function must be defined at that point

What does the Intermediate Value Theorem guarantee for a continuous function on a closed interval?

• The function will take every value between its values at the endpoints

• The function will be differentiable

• The function will have a minimum value

• The function will have a maximum value

Why might a function not have an intercept even if it changes sign over an interval?

• Because it is differentiable

• Because it is a polynomial

• Because it has a jump or asymptote

• Because it is continuous