Understanding Asymptotes

This video tutorial explains how to identify horizontal and slant (oblique) asymptotes in rational functions. It covers bottom heavy functions, where the degree of the denominator is greater than the numerator, resulting in a horizontal asymptote at y=0. It also discusses cases where the degrees are equal, requiring division of coefficients to find the horizontal asymptote. For top heavy functions, the video explains how to find slant asymptotes using long division, provided the degree of the numerator exceeds the denominator by one. The tutorial concludes with practice problems to reinforce the concepts.

What is the horizontal asymptote of a function where the degree of the denominator is greater than the numerator?

• y = x

• y = 1

• y = infinity

• y = 0

If a function is given by 7/x - 3, what is its horizontal asymptote?

• y = 0

• y = 7

• y = 3

• y = -3

For the function 2x - 3 divided by x + 4, what is the horizontal asymptote?

• y = -2

• y = 2

• y = 4

• y = 0

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

• Divide the coefficients

• Subtract the coefficients

• Multiply the coefficients

• Add the coefficients

What is the slant asymptote of a function where the degree of the numerator exceeds the denominator by one?

• y = x + 2

• y = 2x

• y = 0

• y = x - 2

When does a function have no horizontal or slant asymptote?

• When the numerator's degree equals the denominator's

• When the numerator's degree exceeds the denominator's by more than one

• When the numerator's degree is less than the denominator's

• When the function is linear

What is the horizontal asymptote of a function with a numerator degree of 2 and a denominator degree of 1?

• y = 2

• No horizontal asymptote

• y = 1

• y = 0

In the function 5x^4 - 6x + 2 divided by 7x - 3, why is there no slant asymptote?

• The numerator's degree exceeds the denominator's by more than one

• The numerator's degree equals the denominator's

• The numerator's degree is less than the denominator's

• The function is constant

What is the horizontal asymptote of a function where the numerator and denominator have the same degree, and the coefficients are 8 and 4?

• y = 0

• y = 2

• y = 4

• y = 8

For a function with a bottom-heavy structure and an added constant of 4, what is the horizontal asymptote?

• y = 1

• y = -4

• y = 4

• y = 0