Understanding Limits and Horizontal Asymptotes

The video tutorial explains how to use the graph of a function, f(x), to determine limits as x approaches positive and negative infinity. It also covers how to find the equations of horizontal asymptotes by evaluating these limits. The tutorial demonstrates that as x approaches positive infinity, the function approaches a y-value of -3, and as x approaches negative infinity, it approaches a y-value of 3. These values correspond to the horizontal asymptotes y = -3 and y = 3, respectively.

What is the primary focus of the video tutorial?

• Learning about derivatives

• Exploring the concept of limits and horizontal asymptotes

• Studying the properties of integrals

• Understanding vertical asymptotes

As x approaches positive infinity, what value does f(x) approach?

• Negative three

• Positive three

• Positive infinity

• Zero

What is the horizontal asymptote as x approaches positive infinity?

• y = infinity

• y = -3

• y = 3

• y = 0

As x approaches negative infinity, what value does f(x) approach?

• Negative three

• Zero

• Positive three

• Negative infinity

What is the horizontal asymptote as x approaches negative infinity?

• y = infinity

• y = 3

• y = 0

• y = -3

How are horizontal asymptotes determined from limits?

• By using the midpoint theorem

• By calculating the integral

• By finding the derivative

• By evaluating the limits at infinity

What is the equation of the horizontal asymptote when the limit of f(x) as x approaches infinity is negative three?

• y = infinity

• y = 0

• y = -3

• y = 3

What is the equation of the horizontal asymptote when the limit of f(x) as x approaches negative infinity is positive three?

• y = -3

• y = 0

• y = 3

• y = infinity

Why does the graph approach the line y = -3 as x moves to the right?

• Because it is a vertical asymptote

• Because it is a horizontal asymptote

• Because it is a tangent line

• Because it is a secant line

Why does the graph approach the line y = 3 as x moves to the left?

• Because it is a secant line

• Because it is a tangent line

• Because it is a horizontal asymptote

• Because it is a vertical asymptote