Continuity

Find the point or points of discontinuity. If none, state continuous.

 $f\left(x\right)=\frac{5}{x-3}$  

•  $x=3$  hole

•  $x=-3$  VA

•  $x=3$  VA

• Continuous

Tags

CCSS.HSF-IF.C.7D

Find the points of discontinuity and state the type.

 $f\left(x\right)=\frac{x+4}{x^2+10x+24}$  

•  $x=-4\ and\ x=-6$  Both VA's

•  $x=-4\$ VA;  $x=-6$  Hole

•  $x=-4$  Hole; $x=-6$  VA

•  $x=-4\ and\ x=-6$  Both Holes

Tags

CCSS.HSF-IF.C.7D

Find the points of discontinuity and the type

 $f\left(x\right)=x^3-2x^2+x-2$  

• Continuous on it's Domain
  

• Discontinuous  $x=1\ and\ x=-1$  

• Discontinuous  $x=-2,\ x=-1\ and\ x=1$  

• Continuous for all positive values

Tags

CCSS.HSA.APR.B.3

Find the Domain for

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

•  $\left(1,\infty\right]$  

•  $\left[-\infty,\infty\right]$  

•  $\left(-\infty,1\right)$  

•  $\left[-\infty,1\right)$  U $\left(1,\infty\right]$  

Tags

CCSS.HSA.APR.D.7

Find the points of discontinuity and state the type

 $\frac{x^2+4x-5}{x+5}$  

•  $x=1$  hole

•  $x=-5$  VA

•  $x=-5$  Hole

•  $x=1$ VA ; $x=-5$  Hole

Tags

CCSS.HSF-IF.C.7D

Find the Domain of the Function

 $\frac{x^2-1}{x^2-3x+2}$  

•  $\left(-\infty,\infty\right)$  

•  $\left(-\infty,1\right)$  U $\left(1,\infty\right)$  

•  $\left(-\infty,1\right)$  U $\left(1,2\right)$  U $\left(2,\infty\right)$  

•  $\left(-\infty,2\right)$  U $\left(2,\infty\right)$  

Tags

CCSS.HSF.IF.B.5

 $f\left(x\right)=-x^5+2x+1$  

Identify the Continuity of

• Discontinuous with a VA

• Discontinuous with a Hole

• Continuous on the domain  $\left(-\infty,\infty\right)$  

• Continuous on the domain  $\left[0,\infty\right)$  

Tags

CCSS.HSF-IF.C.7D

 Find the points of discontinuity and state the type $f\left(x\right)=\frac{\sqrt{x-2}}{x-2}$  

• Discontinuous  $x=2$  

• Continuous on the Domain  $\left(2,\infty\right)$  

• Continuous on it's Domaind  $\left[2,\ \infty\right)$  

• Continuous on it's Domain  $\left(-\infty,2\right)$  

Tags

CCSS.HSF.IF.B.5

Find the Domain of

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

•  $\left[3,\infty\right)$  

•  $\left(-2,3\right)$  U $\left(3,\infty\right)$  

•  $\left(3,\infty\right)$  

•  $\left(-\infty,\infty\right)$  

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

CCSS.HSF.IF.B.5

Find the Domain  $\frac{x^2}{x^2+100}$ 

•  $\left(-\infty,\ \infty\right)$  

•  $\left(-\infty,-10\right)$  U $\left(-10,\ 10\right)$  U $\left(10,\infty\right)$  

•  $\left[-10,10\right]$  

•  $\left(-\infty,\ -10\right)$  U $\left(10,\ \infty\right)$  

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

CCSS.HSF.IF.B.5