How to identify the asymptotes and intercepts of a rational function

The video tutorial covers the concept of asymptotes in rational functions, focusing on horizontal, vertical, and oblique asymptotes. It explains how to determine the presence of each type of asymptote and the conditions under which they occur. The tutorial also demonstrates the use of long division to find oblique asymptotes and discusses the importance of checking for holes in the function. Additionally, it covers how to find the X and Y intercepts of the function.

What happens when the degree of the numerator is greater than the degree of the denominator in a rational function?

• There is no horizontal asymptote.

• There is a horizontal asymptote.

• There is a hole in the graph.

• There is a vertical asymptote.

How can you confirm the presence of a slant asymptote in a rational function?

• By setting the numerator equal to zero.

• By checking if the degrees of numerator and denominator are equal.

• By factoring and ensuring no terms cancel out.

• By finding the horizontal asymptote first.

What is the purpose of using long division in finding a slant asymptote?

• To simplify the numerator.

• To find the remainder of the division.

• To obtain the quotient, which is the slant asymptote.

• To determine the vertical asymptote.

How do you find the X-intercept of a rational function?

• By dividing the numerator by the denominator.

• By finding the slant asymptote.

• By setting the numerator equal to zero.

• By setting the denominator equal to zero.

What is the Y-intercept of a rational function if the numerator is -4 and the denominator is 2?

• 4

• -4

• 2

• -2