Find vertical and horizontal asymptotes of a rational function

The video tutorial covers key concepts in understanding polynomial degrees, focusing on the importance of arranging polynomials in descending order. It explains horizontal asymptotes when the degree of the denominator is larger than the numerator. The tutorial also delves into vertical asymptotes, emphasizing the need to set the denominator to zero and identify holes through factoring. It highlights the irrelevance of complex solutions for real vertical asymptotes. Finally, the video discusses finding X and Y intercepts in rational functions, including handling square roots and the absence of a Y intercept when division by zero occurs.

What is the horizontal asymptote of a rational function when the degree of the denominator is greater than the degree of the numerator?

• x = 0

• y = 1

• x = 1

• y = 0

When does a vertical asymptote occur in a rational function?

• When the numerator is zero

• When the denominator is zero

• When both numerator and denominator are zero

• When the degrees of numerator and denominator are equal

What is a 'hole' in the context of graphing rational functions?

• A point where the graph crosses the x-axis

• A point where the graph crosses the y-axis

• A point that is undefined due to a common factor in numerator and denominator

• A point where the graph has a vertical asymptote

How do you find the x-intercepts of a rational function?

• Set both numerator and denominator equal to zero

• Set the denominator equal to zero

• Set the numerator equal to zero

• Set the function equal to one

Why might a rational function not have a y-intercept?

• Because the function is undefined at x = 0

• Because the degrees of numerator and denominator are equal

• Because the denominator is zero

• Because the numerator is zero