Graphs of Rational Functions

 $\frac{14+x}{x^2-4}$  

The expression is undefined when x is 

•  $-14\ only$  

•  $2\ only$  

•  $-2\ or\ 2$  

•  $-14,\ 2\ or\ -2$ 

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

For which values of x is the function undefined?

•  $1\ and\ -6$  

•  $2\ and\ 3$  

•  $3\ and\ -2$  

•  $6\ and\ -1$  

 $f\left(x\right)=\frac{x^2-16}{x+4}$  

What is the point of discontinuity for the function?

•  $\left(-4,-8\right)$  

•  $\left(-4,\ 8\right)$  

•  $\left(4,\ 8\right)$  

•  $\left(4,\ -8\right)$  

 $f\left(x\right)=\frac{x^2-25}{x^2-3x-10}$  

What are the asymptotes of the function?

•  $x=1\ and\ y=2$  

•  $x=-1\ and\ y=-2$  

•  $x=-2\ and\ y=1$  

•  $x=-2\ and\ y=-1$  

•  $x=1\ and\ y=1$  

 $f\left(x\right)=\frac{x^2-25}{x^2-3x-10}$  

What are the x-intercepts of the function?

•  $\left(5,\ 0\right)$  

•  $\left(0,\ 2.5\right)$  

•  $\left(2.5,\ 0\right)$  

•  $\left(-5,\ 0\right)$  

•  $\left(-5,\ 0\right)\ and\ \left(5,\ 0\right)$  

 $f\left(x\right)=\frac{9x}{3x-15}$  

Find the domain.

•  $\left(-\infty,\ 5\right)\cup\left(5,\ \infty\right)$  

•  $\left(-\infty,\ 0\right)\cup\left(0,\ \infty\right)$  

•  $\left(-\infty,\ -5\right)\cup\left(-5,\ \infty\right)$  

•  $\left(-\infty,\ \infty\right)$  

•  $\left(-\infty,\ 3\right)\cup\left(3,\ \infty\right)$  

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

What is the y-intercept?

•  $\left(0,\ -6\right)$  

•  $\left(0,\ -3\right)$  

•  $\left(0,\ -2.5\right)$  

•  $\left(0,\ 2\right)$  

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

What type of asymptotes does the function have?

•  $horizontal,\ only$  

•  $vertical,\ only$  

•  $both\ vertical\ and\ horizontal$  

•  $none$  

 $f\left(x\right)=\frac{x-2}{x^2-9}$  

What is the equation of the horizontal asymptote?

•  $y=1$  

•  $y=0$  

•  $none$  

•  $x=3\ and\ x=-3$  

 $f\left(x\right)=\frac{x+2}{3x-6}$  

What is the range of the function?

•  $\left(-\infty,\ \frac{1}{3}\right)\cup\left(\frac{1}{3},\ \infty\right)$  

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

•  $\left(-\infty,\ 3\right)\cup\left(3,\ \infty\right)$  

•  $\left(-\infty,\ \infty\right)$