Function Behavior and Asymptotes

The video tutorial explores the behavior of a graph with respect to its asymptotes. It begins by discussing the need for additional information to understand the graph's shape and behavior. The instructor uses a calculator to evaluate the function near horizontal and vertical asymptotes, demonstrating how to approach these asymptotes from different directions. The tutorial includes a detailed analysis of the graph's behavior near asymptotes, using a table of values and calculator techniques. Finally, the instructor connects different sections of the graph, highlighting intercepts and the overall shape of the graph.

Why is using a calculator recommended for understanding graph behavior?

• It provides a theoretical understanding.

• It offers a practical and reliable approach.

• It is only useful for simple functions.

• It is less reliable than other methods.

How does the function behave as it approaches positive infinity?

• It remains constant.

• It approaches the horizontal asymptote from above.

• It approaches the horizontal asymptote from below.

• It moves away from the horizontal asymptote.

What is the behavior of the function as it approaches negative infinity?

• It remains constant.

• It approaches y = 0 from below.

• It approaches y = 0 from above.

• It moves away from y = 0.

What happens to the function near the vertical asymptote at x = -1?

• It approaches a large negative value on the left.

• It approaches a large positive value on the left.

• It approaches zero.

• It remains constant.

What is the function's behavior just to the right of x = -1?

• It approaches a large positive value.

• It approaches a large negative value.

• It remains constant.

• It approaches zero.

How does the function behave just to the left of the vertical asymptote at x = 1?

• It remains constant.

• It approaches a large negative value.

• It approaches zero.

• It approaches a large positive value.

What is the function's behavior just to the right of x = 1?

• It approaches a large positive value.

• It approaches a large negative value.

• It remains constant.

• It approaches zero.

What shape does the graph take in the middle section?

• A circle.

• A straight line.

• A concave down parabola-like shape.

• A concave up parabola-like shape.

What is the significance of intercepts in graphing this function?

• They are not important.

• They only affect the horizontal scale.

• They only affect the vertical scale.

• They help determine the scale and shape.

What is the overall shape of the graph once all elements are combined?

• A complex rational function shape.

• A simple parabola.

• A simple line.

• A perfect circle.