Asymptotes in Rational Functions

The video tutorial explains rational functions, focusing on asymptotes. It covers vertical, horizontal, and oblique asymptotes, and how to identify them. The role of polynomial degree in determining asymptotes is discussed, along with methods to find horizontal and oblique asymptotes using long division.

What is a rational function?

• A function that can be simplified to a whole number

• A function that has no fractions

• A function that involves a fraction with a variable in the denominator

• A function that is always linear

What is the primary characteristic of a vertical asymptote?

• It shows where the graph approaches infinity

• It indicates where the graph crosses the x-axis

• It is a line that the graph never touches

• It is a point where the function is undefined due to division by zero

How can you determine if a rational function has a vertical asymptote?

• By checking if the numerator equals zero

• By checking if the denominator equals zero

• By finding the highest degree of the numerator

• By finding the highest degree of the denominator

What do horizontal asymptotes indicate about a graph?

• The points where the graph intersects the y-axis

• The behavior of the graph at infinity

• The behavior of the graph at the origin

• The points where the graph intersects the x-axis

How can you tell if a rational function has a horizontal asymptote?

• By checking if the denominator is zero

• By finding the roots of the numerator

• By checking if the numerator is zero

• By comparing the degrees of the numerator and denominator

What happens when the degree of the numerator is less than the degree of the denominator?

• The function has no asymptotes

• The function has a vertical asymptote

• The function has a horizontal asymptote at y=0

• The function has an oblique asymptote

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

• The function has a horizontal asymptote determined by the leading coefficients

• The function has an oblique asymptote

• The function has no asymptotes

• The function has a horizontal asymptote at y=0

What is the significance of the leading coefficient in determining horizontal asymptotes?

• It determines the horizontal asymptote when the degrees are equal

• It determines the y-intercept of the asymptote

• It has no significance

• It determines the slope of the asymptote

How do you find an oblique asymptote?

• By finding the roots of the denominator

• By performing long division on the numerator and denominator

• By setting the denominator equal to zero

• By setting the numerator equal to zero

What is the purpose of long division in finding oblique asymptotes?

• To find the x-intercepts

• To find the remainder

• To simplify the function

• To determine the slope of the asymptote