Graphing rational functions

Which of the following is a vertical asymptote of the function $f\left(x\right)\ =\ -\frac{4}{x^2-3x}$  ?

• x = 4

• x = -4

• x = -3 

• x = 0

What is the horizontal asymptote of the function $f\left(x\right)\ =\ \frac{x-4}{-4x-16}$ ? 

• y =4 

• y = -4

• y = 0

• y = -1/4

• y = 1/4

Which of the following describes the horizontal asymptote of the function? $f\left(x\right)\ =\ \frac{x^3-9x}{3x^2-6x-9}$  

• The horizontal asymptote is y = 0

• The horizontal asymptote is y = 1/3

• There is no horizontal asymptote because the degree of the numerator is greater than the degree of the denominator

• None of the above

Which of the following statements is true about the function below? $f\left(x\right)\ =\ \frac{x^3-9x}{3x^2-6x-9}$  

• There are two vertical asymptotes: x = 3 and x = -1

• There is one vertical asymptote at x = -1 and a hole at x = 3

• There are two holes: x = -3 and x = -1

• There are two vertical asymptotes: x = -3 and x = 1

Which of the following are the correct asymptotes of the function?  $f\left(x\right)\ =\ \frac{3x^2-12x}{x^2-2x-3}$  

• Vertical asymptotes: x = -1 and x = 3
  Horizontal asymptote: y = 3

• Vertical asymptotes: x = 1 and x = -3 
  Horizontal asymptote: y = 0

• Vertical asymptotes: x = -1 and x = 3 
  Horizontal asymptote: N/A

• Vertical asymptotes: x = 1 and x = -3
  Horizontal asymptote: y = 3

Which of the following is not a rational function?

• $\frac{1}{x}$

• $\frac{x}{0}$

• $\frac{x}{x-4}$

• $\frac{4}{x^2}$

Which of the following statements is true about the horizontal asymptote of the function $\frac{3x^2-12x}{x^2-2x-3}$ ?

• There is no horizontal asymptote since the graph passes through what would be horizontal asymptote.

• There is no horizontal asymptote because there is an oblique asymptote.

• The horizontal asymptote is y = 0. However, the graph passes through this point since the degree of the denominator is larger than the degree of the numerator. 

• The horizontal asymptote is y = 3. The graph can pass through this point as long as the end behavior still approaches y = 3 on both sides. 

Which of the following lines is an asymptote of the function below? $f\left(x\right)=\frac{x^3-16x}{-4x^2+4x+24}$  

• x = 3

• y = 0

• y = -1/4

• x = 2

What is the end behavior of the function below? $f\left(x\right)\ =\ \frac{x-2}{x-4}$  

• y = 0 

• y = 1

• y = 2 

• y approaches infinity

Which of the following statements is true about the rational function below?  $f\left(x\right)\ =\ \frac{x^3+x^2}{x^3-4x^2+4x}$  

• There is no horizontal asymptote

• There are two vertical asymptotes at x = 0 and x = 2

• There is a hole at x = 0

• There is one hole and two vertical asymptotes