Understanding Vertical Asymptotes

The video tutorial explains how to determine the equations of vertical asymptotes from a graph. It identifies vertical asymptotes at x = -4 and x = 2 by analyzing the behavior of the function as it approaches these points. At x = -4, the function becomes unbounded from both sides, indicating a vertical asymptote. At x = 2, the function approaches infinity from the left and a finite value from the right, but the unbounded left-hand limit is sufficient to consider it a vertical asymptote.

What is the primary focus when determining vertical asymptotes on a graph?

• The slope of the tangent line

• The points where the function is undefined

• The x-intercepts of the graph

• The y-intercepts of the graph

What happens to the function as it approaches x = -4 from the left?

• It approaches a finite value

• It approaches zero

• It becomes unbounded

• It remains constant

As the function approaches x = -4 from the right, what is observed?

• The function remains constant

• The function becomes unbounded

• The function approaches zero

• The function approaches a finite value

What is the behavior of the function as it approaches x = 2 from the left?

• It approaches a finite value

• It approaches zero

• It becomes unbounded

• It remains constant

What is the significance of a one-sided limit being unbounded?

• It is enough to consider a vertical asymptote

• It suggests a point of discontinuity

• It indicates a horizontal asymptote

• It implies the function is constant

What value does the function approach as x approaches 2 from the right?

• Negative infinity

• A finite value

• Zero

• Infinity

Why is x = 2 considered a vertical asymptote despite the right-hand limit being finite?

• Because the function is defined at x = 2

• Because the left-hand limit is unbounded

• Because the function is continuous at x = 2

• Because the function has a horizontal asymptote at x = 2

Which x-values are identified as having vertical asymptotes in the graph?

• x = -2 and x = 4

• x = 0 and x = 1

• x = -4 and x = 2

• x = 3 and x = 5