Evaluate the limits from a graph with horizontal and vertical asymptotes

The video tutorial explains the concept of vertical and horizontal asymptotes in graphs. It discusses how to determine the behavior of a graph as it approaches these asymptotes from different directions. The tutorial covers left and right hand limits at x = -1, showing how the graph approaches negative and positive infinity. It also examines the behavior near a second vertical asymptote and analyzes the graph's approach to a horizontal asymptote as x moves towards positive and negative infinity.

What happens to the graph as it approaches the vertical asymptote at x = -1 from the left?

• It crosses the asymptote.

• It approaches negative infinity.

• It approaches positive infinity.

• It remains constant.

When approaching the vertical asymptote at x = -1 from the right, what is the behavior of the graph?

• It approaches positive infinity.

• It approaches negative infinity.

• It remains constant.

• It oscillates.

What is the behavior of the graph as it approaches the vertical asymptote at x = 2 from both sides?

• It approaches zero.

• It approaches positive infinity.

• It remains constant.

• It approaches negative infinity.

As x approaches positive infinity, what does the graph approach?

• A vertical asymptote.

• A horizontal asymptote at y = 1.

• A horizontal asymptote at y = 0.

• A constant value.

What is the behavior of the graph as x approaches negative infinity?

• It remains constant.

• It approaches a horizontal asymptote at y = 1.

• It approaches a vertical asymptote.

• It oscillates.