Understanding Intercepts and Asymptotes in Rational Functions

This video tutorial explains how to find the intercepts and asymptotes of a rational function. It begins with a graphical analysis to identify the x and y intercepts, as well as the vertical and horizontal asymptotes. The tutorial then demonstrates how to calculate these intercepts and asymptotes by hand, using function notation and algebraic methods. The video covers the process of setting the numerator and denominator to zero to find intercepts and asymptotes, and compares the degrees of the numerator and denominator to determine horizontal asymptotes.

What is the x-intercept of the rational function as seen on the graph?

• (0, -1.5)

• (1.5, 0)

• (0, 2)

• (-2, 0)

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

• Find the lowest degree of y

• Set y to zero and solve for x

• Set x to zero and solve for y

• Find the highest degree of x

What is the y-intercept of the rational function as seen on the graph?

• (0, 2)

• (0, -1.5)

• (1.5, 0)

• (-2, 0)

What is the equation of the vertical asymptote for the given function?

• x = 1.5

• x = -2

• y = 2

• y = -1.5

Which of the following is true about the vertical asymptote?

• It is found by setting the numerator to zero

• It is found by adding the coefficients

• It is found by setting the denominator to zero

• It is found by equating the degrees of numerator and denominator

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

• By the sum of the coefficients

• By the difference of the coefficients

• By the ratio of the leading coefficients

• By the product of the coefficients

What is the horizontal asymptote of the function as seen on the graph?

• y = 0

• y = 2

• x = -2

• x = 1.5

What is the leading coefficient of the numerator in the given function?

• 2

• 1

• 3

• 0

What happens to the horizontal asymptote if the degree of the numerator is higher than the degree of the denominator?

• It remains unchanged

• It becomes y = 0

• There is no horizontal asymptote

• It becomes x = 0

If the degree of the denominator is higher than the numerator, what is the horizontal asymptote?

• x = 1.5

• y = 2

• y = 0

• x = -2