Understanding Discontinuities in Rational Functions

The video tutorial explains how to identify discontinuities in rational functions by factoring the numerator and denominator. It discusses the types of discontinuities, including removable and non-removable, and provides a graphical interpretation. The tutorial also covers the calculus perspective on limits and discontinuities, highlighting the differences between holes and vertical asymptotes.

What is the first step in determining the discontinuity of a rational function?

• Solving for x values

• Factoring the numerator and denominator

• Calculating the derivative

• Graphing the function

At which x values does the function have discontinuity due to division by zero?

• x = 3 and x = -3

• x = 1 and x = -1

• x = 2 and x = -2

• x = 0 and x = 4

What type of discontinuity occurs when there is a common factor in both the numerator and denominator?

• Removable discontinuity

• Jump discontinuity

• Infinite discontinuity

• Oscillating discontinuity

Which factor results in a removable discontinuity at x = -2?

• x - 2

• x + 6

• x - 6

• x + 2

What is the characteristic of a non-removable discontinuity?

• It results in a vertical asymptote

• It occurs at a common factor

• It is always removable

• It results in a hole in the graph

Which type of discontinuity is associated with a vertical asymptote?

• Infinite discontinuity

• Continuous discontinuity

• Jump discontinuity

• Removable discontinuity

What happens to the function values as x approaches 2 from the left?

• They approach zero

• They remain constant

• They approach positive infinity

• They approach negative infinity

How is the limit defined at a point of removable discontinuity?

• The limit is zero

• The limit does not exist

• The limit exists and equals a specific value

• The limit is infinite

What is the function value as x approaches -2 from both sides?

• Undefined

• Zero

• Negative two

• Positive two

What is the behavior of the function as x approaches 2 from the right?

• The function values remain constant

• The function values approach positive infinity

• The function values approach negative infinity

• The function values approach zero