Asymptotes of a Rational Function

​RATIONAL FUNCTION

​Some text here about the topic of discussion.

Multiple Choice

Which of the following is the domain of the function $$f\left(x\right)=\frac{x}{x+2}$$  ?

• All real numbers except 0

• All real numbers except 2

• All real numbers except -2

Multiple Choice

Which of the following is the range of the function $$f\left(x\right)=\frac{x}{x+2}$$  ?

• All real numbers except 1

• All real numbers except 0

• All real numbers except -2

• All real numbers except 2

Multiple Choice

Which of the following is the x-intercept of the function $$f\left(x\right)=\frac{x}{x+2}$$  

• $$x=1$$  

• $$x=0$$  

• $$x=-2$$  

• $$x=2$$  

Multiple Choice

Which of the following is the y-intercept of the function $$f\left(x\right)=\frac{x}{x+2}$$  ?

• $$y=-2$$  

• $$y=-1$$  

• $$y=0$$  

• $$y=2$$  

Multiple Choice

Which of the following is the domain of the function $$f\left(x\right)=\frac{x+4}{x-8}$$  ?

• All real numbers except -4.

• All real numbers except 4.

• All real numbers except 8.

• All real numbers except -8.

Multiple Choice

Which of the following is the range of the function $$f\left(x\right)=\frac{x+4}{x-8}$$  ?

• All real numbers except -1.

• All real numbers except 1.

• All real numbers except 8.

• All real numbers except -4

Multiple Choice

Which of the following is the x-intercept of the function $$f\left(x\right)=\frac{x+4}{x-8}$$  ?

• $$x=-1$$  

• $$x=1$$  

• $$x=8$$  

• $$x=-4$$  

Multiple Choice

Which of the following is the y-intercept of the function $$f\left(x\right)=\frac{x+4}{x-8}$$ ?

• $$y=1$$  

• $$y=-1$$  

• $$y=-\frac{1}{2}$$  

• $$y=\frac{1}{2}$$  

Multiple Choice

Which of the following is the domain of the function $$f(x)=\frac{3x}{x+3}$$ ?

• All real number except 3 

• All real numbers except -3. 

• All real number except 0. 

• All real numbers. 

Multiple Choice

Which of the following is the range of the function $$f(x)=\frac{3x}{x+3}$$ ?

• All real number except 3 

• All real numbers except -3. 

• All real number except 0. 

• All real numbers. 

Multiple Choice

Which of the following is the x-intercept of the function $$f(x)=\frac{3x}{x+3}$$ ?

• (0,0)

• (-3,0)

• (0,3)

• (3,0)

Multiple Choice

Which of the following is the -intercept of the function $$f(x)=\frac{3x}{x+3}$$ ?

• (0,0)

• (-3,0)

• (0,3)

• (3,0)

Multiple Choice

Which of the following is the vertical asymptote of the function $$f(x)=\frac{3x}{x+3}$$ ?

• x=3

• x=-3

• x=0

• x=-1

Multiple Choice

Which of the following is the horizontal asymptote of $$f(x)=\frac{3x}{x+3}$$ ?

• y=3

• y=-3

• y=o

• None

Multiple Choice

Which of the following is the domain of $$f(x)=\frac{x+6}{x-2}$$ ?

• All real numbers except 6.

• All real numbers except -6.

• All real numbers except 2.

• All real numbers except -2..

Multiple Choice

Which of the following is the range of $$f(x)=\frac{x+6}{x-2}$$ ?

• All real numbers except 6.

• All real numbers except 2

• All real numbers except -2.

• All real numbers except 1.

Multiple Choice

Which of the following is the x-intercept of $$f(x)=\frac{x+6}{x-2}$$ ?

• (-6,0)

• (6,0)

• (-2,0)

• (2,0)

Multiple Choice

Which of the following is the y-intercept of $$f(x)=\frac{x+6}{x-2}$$ ?

• (0,-3)

• (0,3)

• (-3,0)

• (3,0)

Multiple Choice

Which of the following is the vertical asymptote of $$f(x)=\frac{x+6}{x-2}$$ ?

• x=2

• x=-2

• y=-1

• y=1

Multiple Choice

Which of the following is the horizontal asymptote of $$f(x)=\frac{x+6}{x-2}$$ ?

• x=2

• x=-2

• y=-1

• y=1

Multiple Choice

What is the domain of $$f\left(x\right)=\frac{x-2}{x^2-1}$$  ?

• All real numbers except 1 and 2.

• All real numbers except 1 and -1.

• All real numbers except -1 and 2.

• All real numbers except 1

Multiple Choice

What is the x-intercept of $$f\left(x\right)=\frac{x-2}{x^2-1}$$  ?

• (0,2)

• (0,-2)

• (2,0)

• (-2,0)

Multiple Choice

What is the y-intercept of $$f\left(x\right)=\frac{x-2}{x^2-1}$$  ?

• (0,2)

• (0,-2)

• (2,0)

• (-2,0)

Multiple Choice

What is the vertical asymptote of $$f\left(x\right)=\frac{x-2}{x^2-1}$$  ?

• x=2

• x=1

• x=1 and -1

• x=-2 and 2

Multiple Choice

What is the domain of $$f\left(x\right)=\frac{x^2-4}{x+1}$$  ?

• All real numbers except 1.

• All real numbers except -1

• All real numbers except -4.

• All real number except 4.

Multiple Choice

What is the x-intercept of $$f\left(x\right)=\frac{x^2-4}{x+1}$$  ?

• (2,0)

• (-2,0)

• (-2,0) and (2,0)

• (0,-2) and (0,2)

Multiple Choice

What is the y-intercept of $$f\left(x\right)=\frac{x^2-4}{x+1}$$  ?

• (0,-4)

• (0,4)

• (-4,0)

• (4

Multiple Choice

What is the vertical asymptote of $$f\left(x\right)=\frac{x^2-4}{x+1}$$  ?

• x=-2

• x=2

• x=-1

• x=1

Multiple Choice

What is the vertical asymptote of $$f\left(x\right)=\frac{x^2+2x-15}{\left(x+5\right)\left(x-2\right)}$$  ?

• x=2

• x=1

• x=-5

• x=0

Multiple Choice

What is the vertical asymptote of $$f\left(x\right)=\frac{x+3}{x^2-2x-3}$$   ?

• x=-3 only

• x=3 only

• x=3 and x=-1

• x=-3 and x=1

Multiple Choice

What is the horizontal asymptote of $$f\left(x\right)=\frac{x-2}{x^2-1}$$  ?

• y=0

• y=1

• y=-1

• none

Multiple Choice

What is the horizontal asymptote of $$f\left(x\right)=\frac{x^2-4}{x+1}$$  ?

• y=1

• y=0

• None

• y=-1

Multiple Choice

What is the horizontal asymptote of $$f\left(x\right)=\frac{4x^2+2x-15}{\left(x+5\right)\left(x-2\right)}$$  ?

• None

• y=4

• y=0

• x= $$\frac{1}{4}$$  

Multiple Choice

What is the horizontal asymptote of $$f\left(x\right)=\frac{4x+3}{x^2-2x-3}$$   ?

• y=4

• None

• y=0

• y=1

Multiple Choice

What is the horizontal asymptote of $$f\left(x\right)=\frac{1-4x^2}{x^2}$$  ?

• y=1

• y=-1

• y=4

• y=-4