Properties of Rational Functions

 $f\left(x\right)=\frac{x+1}{2x-3}$  
What is the equation of the horizontal asymptote?

•  $y=\frac{1}{2}$  

•  $y=0$  

•  $x=\frac{3}{2}$  

•  $x=-1$  

•  $f\left(x\right)$  does not have a horizontal asymptote

 $f\left(x\right)=\frac{x+1}{4x-2}$  

What is the domain of f(x)?

•  $\left(-\infty,\infty\right)$  

•  $\left(-\infty,-1\right)\cup\left(-1,\infty\right)$  

•  $\left(-\infty,2\right)\cup\left(2,\infty\right)$  

•  $\left(-\infty,\frac{1}{2}\right)\cup\left(\frac{1}{2},\infty\right)$  

 $f\left(x\right)=\frac{3\left(x+2\right)\left(x-1\right)}{\left(x-1\right)\left(x-2\right)}$  
Which of the following is false?

•  $f\left(x\right)\$ has a vertical asymptote on the line  $x=2$  .

•  $f\left(x\right)$  does not have a horizontal asymptote.

•  $f\left(x\right)$  has a hole at the point  $\left(1,-9\right)$  

•  $f\left(x\right)$  crosses the  $x-$  axis at  $x=-2$  

 $f\left(x\right)=\frac{3x^4-6x+12}{2x+5x^4}$  

What is the equation of the horizontal asymptote?

•  $y=0$  

•  $y=\frac{3}{2}$  

•  $y=\frac{3}{5}$  

•  $f\left(x\right)$  does not have a horizontal asymptote.

Which of the following rational functions could be the graph shown?

• $f\left(x\right)=\frac{2\left(x-1\right)}{\left(x+2\right)}$

• $f\left(x\right)=\frac{2\left(x-4\right)\left(x-1\right)}{x\left(x-4\right)}$

• $f\left(x\right)=\frac{2\left(x-4\right)\left(x-1\right)}{\left(x-4\right)\left(x+2\right)}$

• $f\left(x\right)=\frac{2\left(x+2\right)\left(x-4\right)}{\left(x-4\right)\left(x+1\right)}$

 $f\left(x\right)=\frac{\left(x+2\right)\left(x-2\right)}{x^2-2x-8}$  
Which of the following statements is true?

• f(x) has two x-values at which there is a hole in the graph.

• f(x) has two x- intercepts.

• f(x) is continuous for all values of x.

• f(x) has one hole in the graph and one vertical asymptote.

• f(x) does not have a horizontal asymptote.

 $f\left(x\right)=\frac{\left(3x-1\right)\left(x+2\right)}{x^2-x-6}$  
What does the graph of f(x) look like at  $x=3$  ?

• f(x) has a hole in the graph at x=3.

• f(x) is continuous at x=3.

• f(x) has a vertical asymptote at x=3.

• The graph crosses the x-axis at x=3

Which of the following have a a horizontal asymptote on the line y=0 and a vertical asymptote on the line x=2?

• $f\left(x\right)=\frac{3\left(x-1\right)}{\left(x-1\right)\left(x-2\right)}$

• $f\left(x\right)=\frac{\left(x-1\right)\left(x+3\right)}{x\left(x-2\right)}$

• $f\left(x\right)=\frac{3\left(x-2\right)}{\left(x+1\right)}$

• $f\left(x\right)=\frac{\left(x-5\right)\left(x-3\right)}{\left(x+2\right)\left(x-1\right)\left(x-7\right)}$