Find the asymptotes and intercepts of a rational function

The video tutorial covers the concept of asymptotes and polynomial division. It begins with an introduction to asymptotes and the process of dividing polynomials using long division. The instructor explains how to handle remainders and rewrite quotients. The tutorial then focuses on identifying vertical and horizontal asymptotes and finding X and Y intercepts using shortcuts. The video emphasizes understanding the mathematical processes and provides practical examples to illustrate the concepts.

What is the main reason the instructor prefers long division over synthetic division?

• It is more accurate.

• It is quicker.

• It is easier to understand.

• It is more fun.

What is the remainder when dividing 4X by 2X?

• 1

• 2

• -5

• 0

How is the vertical asymptote determined from the expression?

• By factoring out constants.

• By identifying the transformations.

• By setting the numerator to zero.

• By setting the denominator to zero.

What is the horizontal asymptote of the graph after transformation?

• Y = -1

• Y = 0

• Y = 1

• Y = 2

What shortcut does the instructor suggest for finding the X intercept?

• Using synthetic division.

• Using the original equation.

• Setting the numerator to zero.

• Setting the denominator to zero.

How can you find the Y intercept of a rational expression?

• By dividing the numerator by the denominator.

• By using synthetic division.

• By setting Y to zero.

• By setting X to zero.

What happens to the graph when the numerator is set to zero?

• The X intercept is found.

• The graph shifts down.

• The graph shifts up.

• The Y intercept is found.