What is the domain of the function? (using inequality notation) s ( t ) = 3 3 t − 10 s\left(t\right)=\frac{3}{\sqrt{3t-10}} s ( t ) = 3 t − 1 0 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> 3

t > 10 3 t>\frac{10}{3} t > 3 1 0

t ≤ 10 3 t\le\frac{10}{3} t ≤ 3 1 0

What is the domain of the function? (using inequality notation) f ( x ) = x x 56 − 4 x f\left(x\right)=\frac{x}{x\sqrt{56-4x}} f ( x ) = x 5 6 − 4 x <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> x

x < 14 , x ≠ 0 x<14,\ x\ne0 x < 1 4 , x  = 0

x ≤ 14 , x ≠ 0 x\le14,\ x\ne0 x ≤ 1 4 , x  = 0

x > − 14 , x ≠ 0 x>-14,\ x\ne0 x > − 1 4 , x  = 0

x > 0 , x > 14 x>0,\ x>14 x > 0 , x > 1 4

Identify the domain of the function. v ( t ) = 3 t t 9 t − 3 v\left(t\right)=\frac{3t}{t\sqrt{9t-3}} v ( t ) = t 9 t − 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> 3 t

t ≤ 1 3 , t ≠ 0. t\le\frac{1}{3},\ t\ne0. t ≤ 3 1 , t  = 0 .

t ≥ 1 3 t\ge\frac{1}{3} t ≥ 3 1

w ( x ) = 10 x + 30 10 w\left(x\right)=\frac{10x+30}{10} w ( x ) = 1 0 1 0 x + 3 0 Identify the domain AND classify the discontinuity of the function

x > 10 x>10 x > 1 0 continuous on the domain

R , x ≠ 10 R,\ x\ne10 R , x  = 1 0 x=10 is a hole

R , x ≠ 3 R,\ x\ne3 R , x  = 3 x = 3 is a vertical asymptote

g ( x ) = 2 − x x − 4 g\left(x\right)=\frac{\sqrt{2-x}}{x-4} g ( x ) = x − 4 2 − x <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> Identify the domain of the function AND classify each discontinuity.

x ≤ 2 x\le2 x ≤ 2 continuous on its domain

x < − 2 , x ≠ 4 x<-2,\ x\ne4 x < − 2 , x  = 4 x = 4 is a vertical asymptote

x ≥ − 2 , x ≠ 4 x\ge-2,\ x\ne4 x ≥ − 2 , x  = 4 x = 4 is a hole

R , x ≠ 2 , x ≠ 4 R,\ x\ne2,\ x\ne4 R , x  = 2 , x  = 4 x =2 is a hole, x = 4 is a vertical asymptote

What is the domain of the function? v ( t ) = t + 1 t − 2 v\left(t\right)=\frac{\sqrt{t+1}}{t-2} v ( t ) = t − 2 t + 1 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

t ≥ − 1 , t ≠ 2 t\ge-1,\ t\ne2 t ≥ − 1 , t  = 2

t > 2 , t ≠ − 1 t>2,\ t\ne-1 t > 2 , t  = − 1

t > − 1 , t ≠ 2 t>-1,\ t\ne2 t > − 1 , t  = 2

3.1 Discontinuity and Domain Practice

Authored by Joseph Collins

Mathematics

10th - 12th Grade

CCSS covered

Used 44+ times

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15 questions

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MULTIPLE SELECT QUESTION

2 mins • 1 pt

What are the types of discontinuities (select all that apply)?
(HINT: Check your notes)

holes (removeable)

asymptotes (non-removeable)

irrational

continuous on the domain

Tags

CCSS.HSF-IF.C.7D

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

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.HSF-IF.C.7D

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

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.HSF-IF.C.7D

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

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.HSF-IF.C.7D

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

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

Tags

CCSS.HSF-IF.C.7D

MULTIPLE SELECT QUESTION

2 mins • 1 pt

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

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

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.REI.A.2

CCSS.HSA.CED.A.3

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

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.REI.A.2

CCSS.HSA.CED.A.3

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

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.7

CCSS.HSA.APR.D.6

10.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

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

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3.1 Discontinuity and Domain Practice

What are the types of discontinuities (select all that apply)?(HINT: Check your notes)

Find and classify each discontinuity of the function. f(x)=xx+5f\left(x\right)=\frac{x}{x+5}f(x)=x+5x​

Find and classify the discontinuity of the function. g(x)=15+5xg\left(x\right)=\sqrt{15+5x}g(x)=15+5x​

Find and classify the discontinuities of the function. h(t)=2t2+2tt3−11t2+24th\left(t\right)=\frac{2t^2+2t}{t^3-11t^2+24t}h(t)=t3−11t2+24t2t2+2t​

Find and classify the discontinuity of the function. f(x)=1x2+9f\left(x\right)=\frac{1}{x^2+9}f(x)=x2+91​

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

What is the domain of the function? (using inequality notation) w(x)=5x−55w\left(x\right)=\frac{\sqrt{5x-5}}{5}w(x)=55x−5​​

What is the domain of the function? (using inequality notation) s(t)=33t−10s\left(t\right)=\frac{3}{\sqrt{3t-10}}s(t)=3t−10​3​

What is the domain of the function? (using inequality notation) f(x)=xx56−4xf\left(x\right)=\frac{x}{x\sqrt{56-4x}}f(x)=x56−4x​x​

What is the domain of the function? (using inequality notation) g(x)=x2+4x−5g\left(x\right)=x^2+4x-5g(x)=x2+4x−5

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What are the types of discontinuities (select all that apply)?
(HINT: Check your notes)

Find and classify each discontinuity of the function.
$f\left(x\right)=\frac{x}{x+5}$

Find and classify the discontinuity of the function.
$g\left(x\right)=\sqrt{15+5x}$

Find and classify the discontinuities of the function.
$h\left(t\right)=\frac{2t^2+2t}{t^3-11t^2+24t}$

Find and classify the discontinuity of the function.
$f\left(x\right)=\frac{1}{x^2+9}$

What is the domain of the function? (using inequality notation)
$w\left(x\right)=\frac{\sqrt{5x-5}}{5}$

What is the domain of the function? (using inequality notation)
$s\left(t\right)=\frac{3}{\sqrt{3t-10}}$

What is the domain of the function? (using inequality notation)
$f\left(x\right)=\frac{x}{x\sqrt{56-4x}}$

What is the domain of the function? (using inequality notation)
$g\left(x\right)=x^2+4x-5$