Asymptotes: 동영상 및 연습문제

Identify which of the following rational functions has no vertical asymptotes.

Consider the given rational function and find vertical asymptotes and values of x corresponding to holes(if applicable). 

f(x) = (x² -49)/(x +7)

Consider the given rational function and find its domain. 

f(x) = 7x²/(x -8)(x +2)

For the following function, write the equation for the vertical asymptote.

f(x) = (x + 8)/(x + 11)

For the following function, write the equations for the vertical, horizontal or oblique asymptotes.

f(x) = (x² - 5x - 13)/(4x² - x - 18)

For the following rational function, graph. f(x) = 5x/(x² - x - 12)

Which of the following best describes an asymptote in the context of rational functions?

Given the function f(x) = 1/x, what are the horizontal and vertical asymptotes?

Using arrow notation, describe the end behavior of f(x) = 1/x as x approaches infinity.

Determine the horizontal asymptote of f(x) = (3x^2 + 2)/(x^2 - 1).

Identify the location of the hole in the function f(x) = (x^2 - 1)/(x - 1).

Describe the behavior of f(x) = 1/(x - 2) as x approaches 2 from the left and right.

How do vertical asymptotes affect the domain of a rational function?

Graph the function f(x) = (x^2 - 1)/(x^2 - 4) and identify its asymptotes.

Using arrow notation, describe the end behavior of f(x) = (2x)/(x + 1) as x approaches infinity.

What is the vertical asymptote of f(x) = 1/(x - 5)?

Determine the horizontal asymptote of f(x) = (5x^3)/(2x^3 + 1).