Horizontal and Vertical asymptotes of rational functions

The video tutorial covers the concepts of degrees in numerators and denominators, explaining how to handle cases where the degree in the denominator is larger. It discusses horizontal and vertical asymptotes, including how to identify them and the importance of considering discontinuities. The tutorial also demonstrates solving for asymptotes and intercepts in rational expressions, emphasizing the need to account for both positive and negative solutions.

What is the degree of a constant term in a polynomial?

• 2

• 0

• 1

• It doesn't have a degree

How do you determine the horizontal asymptote of a rational function when the degree of the denominator is greater than the numerator?

• The horizontal asymptote is 1

• There is no horizontal asymptote

• The horizontal asymptote is the ratio of leading coefficients

• The horizontal asymptote is 0

What must be true for a vertical asymptote to exist in a rational function?

• The function must be undefined

• Both numerator and denominator must be zero

• The denominator must be zero

• The numerator must be zero

When solving for vertical asymptotes, why is it important to check for discontinuities?

• To determine the y-intercepts

• To identify potential holes in the graph

• To ensure the function is continuous

• To find the x-intercepts

How can you find the y-intercept of a rational function?

• Subtract the constant term of the denominator from the constant term of the numerator

• Set the numerator equal to zero

• Set the denominator equal to zero

• Divide the constant term of the numerator by the constant term of the denominator