Asymptotes and Intercepts of a Rational Function

The video tutorial explains how to determine horizontal and vertical asymptotes in rational functions. It covers the importance of leading coefficients for horizontal asymptotes and solving the denominator for vertical asymptotes. The tutorial also discusses identifying holes in the graph and factoring quadratics into binomials. Finally, it explains how to find x and y intercepts, emphasizing the importance of checking for holes and using different methods for solving.

What is the horizontal asymptote when the degrees of the numerator and denominator are equal?

• The ratio of the leading coefficients

• The sum of the leading coefficients

• The difference of the leading coefficients

• The product of the leading coefficients

How do you determine the vertical asymptote of a rational function?

• Set the numerator equal to zero

• Set both numerator and denominator equal to zero

• Set the denominator equal to zero

• Set the leading coefficients equal to zero

What should you check for when finding vertical asymptotes to ensure accuracy?

• Check for holes in the graph

• Ensure the degrees of numerator and denominator are equal

• Ensure the numerator is in standard form

• Verify the leading coefficient is positive

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

• Set the numerator equal to zero

• Set the leading coefficients equal to zero

• Set the denominator equal to zero

• Set both numerator and denominator equal to zero

What is a quick method to find the y-intercept of a rational function?

• Set the numerator equal to zero

• Take the constant term of the numerator over the constant term of the denominator

• Plug zero into all x terms

• Set the denominator equal to zero