Rationals: Discontinuity & Asymptotes

Identify the point(s) of discontinuity.

 $f\left(x\right)=\frac{4}{x-6}$  

• x = 0

• x = 6

• x = -6

• x = 4

Tags

CCSS.HSF-IF.C.7D

Identify the point(s) of discontinuity.

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

• Only x = 2

• Only x = -2

• Only x = 3

• x = 2 and x = 3

• x = -2 and x = 3

Tags

CCSS.HSF-IF.C.7D

Identify the point(s) of discontinuity.

 $f\left(x\right)=\frac{x-1}{3x^2-3}$  

• Only x = 1

• Only x = -1

• Only x = 3

• x = -1 and x = 1

• x = 1 and x = 3

Tags

CCSS.HSF-IF.C.7D

Determine the vertical asymptote(s) for the following function.

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

• x = -3

• x = 5

• x = -3 and x = 5

• x = 0

• Does Not Exist

Tags

CCSS.HSF-IF.C.7D

Determine the vertical asymptote(s) for the following function.

 $f\left(x\right)=\frac{2x}{x-7}$  

• x = 0

• x = 2

• x = 7

• x = -7

• Does Not Exist

Tags

CCSS.HSF-IF.C.7D

Determine the removable point(s) of discontuity (or holes) for the following function.

 $f\left(x\right)=\frac{3x-6}{x^2-9x+14}$  

• x = 2

• x = 7

• x = 2 and x = 7

• x = 0

• Does Not Exist

Tags

CCSS.HSF-IF.C.7D

Determine the horizontal asymptote(s) for the following function.

 $f\left(x\right)=\frac{2x^3+5x-1}{4x^3-2x^2}$  

• y = 0

• y = 2

• y = 4

• y = 1/2

• Does Not Exist

Tags

CCSS.HSF-IF.C.7D

Determine the horizontal asymptote(s) for the following function.

 $f\left(x\right)=\frac{2x-5}{x^2-1}$  

• y = 2

• y = 1

• y = -1

• y = 0

• Does Not Exist

Tags

CCSS.HSF-IF.C.7D

Determine the horizontal asymptote(s) for the following function.

 $f\left(x\right)=\frac{4x^3}{x^2-9}$  

• y = 4

• y = 3

• y = -3

• y = 0

• Does Not Exist

Tags

CCSS.HSF-IF.C.7D

Determine all removable points of discontinuity (holes), vertical asympotes, and horizontal asympotes for the following function.

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

• Holes: x = -3
  Vertical: x = 1/2
  Horizontal: y = 0

• Holes: x = 1/2
  Vertical: x = -3
  Horizontal: y = 0

• Holes: Do Not Exist
  Vertical: x = 1/2 and x = -4
  Horizontal: y = 1

• Holes: x = 1/2
  Vertical: x = -3
  Horizontal: y = 1

• Holes: x = -3
  Vertical: x = 1/2
  Horizontal: Does Not Exist

Tags

CCSS.HSF-IF.C.7D