Vertical, Horizontal, and Slant Asymptotes

Which asymptote(s) are determined by looking at the denominator?

• vertical
• horizontal
• slant
• none

Tags

CCSS.HSF-IF.C.7D

When finding the Horizontal asymptotes of a function, you should be thinking...

• "Set Bottom = to Zero"
• "Top = 0"
• "f(0)"
• "Look at the Degree of the top and bottom..."

Tags

CCSS.HSA.APR.D.6

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

What are the asymptotes?

• x=-2 and y=-1
• x=-2 and y=1
• x=2 and y=1
• x=2 and y = -1

Tags

CCSS.HSF-IF.C.7D

What is the vertical asymptote?

 $y=\frac{\left(x-5\right)\left(x+5\right)}{\left(x-5\right)\left(x+4\right)}$  

• x= 4

• x= -4

• x= 5

• x= -5

Find the horizontal asymptote.

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

• y = -2

• none

• y = 0

• y = 1/2

What type(s) of asymptotes does this function have? (Check all that apply.)

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

• Vertical

• Horizontal

• Oblique

Does the function have a slant asymptote?
 $y=\frac{4x^4+x^3-10x^2-4x+15}{9x^3+2x^{2\ }-4x+12}$  

• Yes

• No

Does the function have a horizontal asymptote, slant asymptote, or neither?
 $y=\frac{2x^2+8x-11}{5x-8}$  

• Horizontal

• Slant

• Neither