Asymptotes: 동영상 및 연습문제

Consider the given rational function and find its domain. 

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

Consider the given rational function and find its domain. 

f(x) = 7x²/(x -8)(x +2)

Consider the given rational function and find its domain. 

f(x) = (x +12)/(x² -144)

Identify the graph of the rational function having domain as (-∞, 5) U (5, ∞).

Complete the given statement using the graph of the rational function in the figure shown. 

As x → 14⁺, f(x) →

Complete the given statement using the graph of the rational function in the figure shown. 

As x → +∞ , f(x) →

Complete the given statement using the graph of the rational function in the figure shown.

As x → -8⁺, f(x) →

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

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

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

f(x) = (x² -49)/(x +7)

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

f(x) = 1/(x + 13)

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

f(x) = (x -7)/(x² -49)

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

f(x) = (x +3)/(x² -2x -15)

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

f(x) = (x² - 9)/(x + 17)

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

f(x) = (x² + 16)/(x - 8)

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

f(x) = (x² - 5x - 13)/(4x² - x - 18)

Graph the given rational function using the transformation of f(x) = 1/x. g(x) = (1/x) +8

Graph the given rational function using the transformation of f(x) = 1/x. g(x) = 1/(x +6) -1

Identify the graph of the following rational function through the way it approaches a vertical asymptote x = 4.

f(x) = -1/(x - 4)²

Graph the given rational function using the transformation of f(x) = 1/x². g(x) = 1/(x +3)² 

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

For the graph of the rational function given below, identify any vertical, horizontal, or oblique asymptotes. Also, write the domain of the function.

For the graph of the rational function given below, identify any vertical, horizontal, or oblique asymptotes. Also, write the domain of the function.

For the following rational function, graph. f(x) = (x + 2)/(x - 7)

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

Graph the given rational function following the seven steps. f(x)=(x+4)/(x²-x−12)

Graph the given rational function following the seven steps. f(x)=(x−8)/(x²−16)

The characteristics of the graph of a rational function f are given below. Find f(x).

x-intercepts: (6, 0) and (8, 0)

One of the vertical asymptotes: x = 5

horizontal asymptote: y = 6

The characteristics of the graph of a rational function f are given below. Find f(x).

x-intercepts: (0, 0)

vertical asymptotes: x = -2 and x = 2

horizontal asymptote: y = 0

Graph the given rational function following the seven steps. f(x)= 3x⁴/(x²+13)

The graph of a rational function f is given below. Find f(x).