Rational Functions Review

Does this function have any vertical asymptotes? If so, what are their equations? $y=\frac{x+7}{x^2+9x+14}$  

• No vertical asymptotes.

• Two vertical asymptotes: x = -7 and x = -2 

• One vertical asymptote: x = -7

• One vertical asymptote: x = -2

Does this function have any holes? If so, where? $y=\frac{x+7}{x^2+9x+14}$  

• No holes.

• One hole: at x = -7

• One hole: at x = 7 

• Two holes: at x = -2 and x = -7

Does this function have any vertical asymptotes? If so, what are their equations? $y=\frac{\left(x+3\right)\left(x-4\right)\left(x+7\right)}{\left(x-4\right)}$   

• No vertical asymptotes.

• One vertical asymptote: x = 4

• Two vertical asymptotes: x = -3 and x = -7

• Three vertical asymptotes:  x = -3, x = 4, and x = -7

Does the function have any holes? If so, what are their coordinate pairs? $y=\frac{\left(x+3\right)\left(x-4\right)\left(x+7\right)}{x-4}$   

• No holes

• One hole: at x = 4

• One hole: at x = -4

• Two holes: at x = -3 and x = -7

• None

• x = -4

• x = 3

• x = 4

A rational function is ...?

• a line that continually approaches a given curve but does not meet it at any finite distance.

• The top of a rational expression

• The bottom of a rational expression

• Made up of a ratio (fraction) of two polynomials

What is the vertical asymptote of the function below?

 $f\left(x\right)=\frac{x^2-2x-8}{x^2+2x-24}$  

•  $y=1$  

•  $x=4$  

•  $x=-2$  

•  $x=-6$  

What is the horizontal asymptote, if any, of the function below?

 $f\left(x\right)=\frac{x+6}{x^2+9x+18}$  

•  $y=1$  

•  $y=0$  

•  $x=-3$  

• none
  

Which, if any, of the points is a hole of $f(x)?$  

 $f\left(x\right)=\frac{6x+12}{x^2+7x+10}$  

• A hole exists on  $f\left(x\right)$  where  $x=-2$  

• A hole exists on  $f\left(x\right)$  where  $x=-5$  

• A hole exists on  $f\left(x\right)$  where  $x=6$  

• The function does not have any holes.

Determine if the rational function has a vertical asymptote, a hole, both, or neither.

 $f\left(x\right)=\frac{x^2-3x}{x^2-9}$  

• Vertical Asymptote

• Hole

• Both

• Neither