3.1 Discontinuity and Domain Practice

What are the types of discontinuities (select all that apply)?

(HINT: Check your notes)

• holes (removeable)

• asymptotes (non-removeable)

• irrational

• continuous on the domain

Find and classify each discontinuity of the function.

 $f\left(x\right)=\frac{x}{x+5}$  

• x = 5, vertical asympotoe 

• x = -5, hole 

• x = -5, vertical asymptote

• continuous on the domain

Tags

CCSS.HSA.APR.D.7

CCSS.HSA.REI.D.10

Find and classify the discontinuity of the function.

 $g\left(x\right)=\sqrt{15+5x}$  

• x= 3, hole

• x = -3 hole 

• x = -3, vertical asymptote

• continuous on the domain

Tags

CCSS.HSA.REI.D.11

Find and classify the discontinuities of the function.

 $h\left(t\right)=\frac{2t^2+2t}{t^3-11t^2+24t}$  

• t=0, hole;
  t=3, t=8 vertical asymptotes

• t=0, vertical asymptote;
  t=3, t=8, holes

• t=0, hole
  t = -1, vertical asymptote. 

• t=-8, hole; 
  t=0, t = -3, vertical asymptotes. 

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.APR.D.6

Find and classify the discontinuity of the function.

 $f\left(x\right)=\frac{1}{x^2+9}$  

• x=3, x=-3, vertical asymptotes

• x=3, x=-3, hole

• x=3, hole
  x=-3, vertical asymptotes

• continuous on the domain

What should you be looking for when trying to determine the domain of the function? (Select all that apply)

• even radicals can't be negative.

• the value of the input can't be greater than the value of the output.

• cannot divide by zero.

• domain can't contain fractions.

Tags

CCSS.HSA.APR.D.7

What is the domain of the function? (using inequality notation)

 $w\left(x\right)=\frac{\sqrt{5x-5}}{5}$  

•  $x>1$  

•  $x\ge1$  

•  $x<5$  

•  $x<-1$  

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.REI.A.2

What is the domain of the function? (using inequality notation)

 $s\left(t\right)=\frac{3}{\sqrt{3t-10}}$  

•  $t>\frac{10}{3}$  

•  $t\le\frac{10}{3}$  

•  $t>4$  

• all real numbers

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.REI.A.2

What is the domain of the function? (using inequality notation)

 $f\left(x\right)=\frac{x}{x\sqrt{56-4x}}$  

•  $x\le14,\ x\ne0$  

•  $x<14,\ x\ne0$  

•  $x>-14,\ x\ne0$  

•  $x>0,\ x>14$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

What is the domain of the function? (using inequality notation)

 $g\left(x\right)=x^2+4x-5$  

•  $-5<x<1$  

•  $x\ne1,\ x\ne-5$  

•  $x\ge1$  

• all real numbers

Tags

CCSS.HSA.REI.D.10