Discontinuities- Holes and Vertical Asymptotes

What is the definition of an ASYMPTOTE?

• A curved line. 
• A line that only touches the origin. 
• A line that only lives on the first quadrant. 
• A line that a curve approaches, as it heads towards infinity. 

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

The equation of a vertical asymptote is written in the form:

• x=

• y=

• none of the above

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CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

Which of the following is determined by just looking at the denominator?

• vertical asymptote
• horizontal asymptote
• holes
• slant asymptote

Find the vertical asymptote.

 $g\left(x\right)=\frac{\left(x+3\right)\left(x-2\right)}{\left(x+5\right)\left(2x-1\right)}$  

• x=-5

• x=1/2

• x=-1/2

• x=-3

• x=2

Tags

CCSS.HSA.APR.D.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

The holes of a rational function occur when :

• my pencil pokes a hole in the paper I'm working on
• there is something left in the denominator
• the value of f(0)
• a factor in the denominator cancels with a factor in the numerator

Tags

CCSS.HSA.APR.B.2

CCSS.HSA.APR.D.7

What is the x-value of the hole? $g\left(x\right)=\frac{\left(x-2\right)\left(x+6\right)}{\left(x+2\right)\left(x-2\right)}$  

• 2

• -2

• -6

• 6

Tags

CCSS.HSA.APR.B.3

 $f\left(x\right)=\frac{\left(x+7\right)\left(x-3\right)\left(x+1\right)}{\left(x-3\right)\left(x-5\right)}$  

Select all of the true statements.

• A hole occurs where x=3

• vertical asymptote at x=3

• vertical asymptote at x=5

• A hole occurs where x=5

Tags

CCSS.HSA.APR.B.3

State the vertical asymptote: 

 $g\left(x\right)=\frac{\left(x+2\right)}{\left(2x+3\right)}$  

• x=2

•  $x=\frac{2}{3}$  
  

•  $x=-\frac{2}{3}$  
  

• x=-2

•  $x=-\frac{3}{2}$  

Tags

CCSS.HSA.APR.D.7

 $h\left(x\right)=\frac{x\left(x-3\right)\left(x-6\right)\left(x+3\right)}{3x\left(x+3\right)\left(x-6\right)\left(x+7\right)}$  

Identify the x-value of the hole(s).

• x=0

• x=-3

• x=6

• x=-7

• x=3

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7