Zeros of Polynomials and Graphing Rational Functions

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

What is the x-intercept of the rational function

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

This function has _______________ asymptotes.
choose all that apply

• horizontal

• slant

• vertical

• no

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

The y-intercept of this function is 

•  $y=5$ 

•  $y=-5$  

•  $y=1$ 

•  $y=3$  

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

The horizontal asymptote is at y = _______

 $f\left(x\right)=\frac{x^2-5x-24}{\left(x+3\right)x^2-3x+2}$  
Check all that apply
This function has:

• hole(s)

• vertical asymptote(s)

• horizontal asymptote

• slant asymptote

• none of these

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)

Tags

CCSS.HSF-IF.C.7D

 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

Tags

CCSS.HSF-IF.C.7D

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)