Multiple Examples on determining the asymptotes of rational functions

The video tutorial covers rational functions, focusing on graphing techniques, reciprocal functions, and the role of polynomials in rational functions. It explains discontinuities, including vertical asymptotes and holes, and delves into horizontal and oblique asymptotes. The tutorial emphasizes the importance of understanding the degree and leading coefficient of polynomials in these contexts.

What is the parent function of a reciprocal function?

• X^3

• 1/X^2

• 1/X

• X^2

Why is it important to have polynomials in standard form?

• To ensure they are polynomials

• To identify the degree and leading coefficient

• To make them easier to read

• To simplify calculations

What happens when the denominator of a rational function equals zero?

• The function has a vertical asymptote or a hole

• The function becomes linear

• The function is undefined

• The function has a horizontal asymptote

When does a horizontal asymptote occur at y = 0?

• When the numerator is a constant

• When the degrees of the numerator and denominator are equal

• When the degree of the denominator is greater than the degree of the numerator

• When the degree of the numerator is greater than the degree of the denominator

How do you determine the horizontal asymptote when the degrees of the numerator and denominator are equal?

• By multiplying the coefficients

• By adding the coefficients

• By subtracting the degrees

• By dividing the leading coefficients

What is the result when the degree of the numerator is greater than the degree of the denominator?

• A horizontal asymptote exists

• The function is undefined

• No horizontal asymptote exists

• A vertical asymptote exists

What is another name for an oblique asymptote?

• Curved asymptote

• Horizontal asymptote

• Slant asymptote

• Vertical asymptote

How do you find an oblique asymptote?

• By factoring the numerator

• By using long division

• By setting the denominator to zero

• By finding the leading coefficient

What should you do first when identifying a slant asymptote?

• Calculate the derivative

• Set the numerator to zero

• Find the horizontal asymptote

• Check if the function can be factored

What is the next step after reviewing asymptotes and rational functions?

• Identifying features of rational function graphs

• Graphing linear functions

• Finding the roots of polynomials

• Solving quadratic equations