Graphing Rational Functions

Select ALL the information that applies to the given rational function.
 $f\left(x\right)=\frac{x-3}{-2x^2+8x-6}$  

• Vertical Asymptote. at x = 1

• No Holes

• Horizontal Asymptote. at y = 0

• y-intercept at (0, 1/2)

Select ALL the information that applies to the given rational function. $f\left(x\right)=\frac{2x^2-2}{x^2-4x+3}$  

• Vertical Asymptote. at x = -3 and x = 1

• Hole at (1, 0)

• Horizontal Asymptote at y = 2

• x-intercepts at (3,0) and (1, 0)

Select ALL the information that applies to the given rational function. $f\left(x\right)=\frac{x^2-x}{-4x+16}$  

• Vertical Asymptote. at x = -1

• No Holes

• Horizontal Asymptote. at y = -1/4

• x-intercepts at (0,0) and (-1,0)

Select ALL the information that applies to the given rational function.  $f\left(x\right)=\frac{x+3}{-3x+6}$  

• Vertical Asymptote at x = 2

• No Holes

• Horizontal Asymptote at y = -1/3

• y-intercepts at (0, 1/2)

 Select ALL the information that applies to the given rational function. $f\left(x\right)=\frac{1}{-3x^2-9}$ 

• No Vertical Asymptote

• No Holes

• Slant (Oblique) Asymptote at  $y=x-3$  

• No x-intercept

Select ALL the information that applies to the given rational function. $f\left(x\right)=\frac{x^3+2x^2-3x+5}{x^2-3x+4}$  

• Vertical Asymptote at x = 3 and x = -1

• No Holes

• Slant (Oblique) Asymptote at y = x + 5

• y-intercept at (0,0)

Graph the function.

 $f\left(x\right)=\frac{-x+1}{x-4}$  

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 Graph the function.

 $f\left(x\right)=\frac{-2x^2+2x+24}{x^3-x^2-12x}$ 

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 $f\left(x\right)=\frac{2x^2+x+1}{x+1}$  Graph the function.

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Match the graph to the correct rational equation below.

• $f(x)=\frac{x^2}{x^2+x-12}$

• $f(x)=\frac{4x^2}{x^2-x-12}$

• $f(x)=\frac{2x^2-2}{2x^2}$

• $f(x)=\frac{x}{x^2+x-12}$