Continuity Date Period
Kuta Software - Infinite Calculus
Name___________________________________
Continuity
Date________________ Period____
Find the intervals on which each function is continuous.
1) f ( x) =
{
x 2 + 2 x + 1, x < 1
x
? ,
2
2) f ( x) =
x¡Ý1
10
f
{
1, x ¡Ù 5
3, x = 5
f
8
8
6
6
4
4
2
2
?2
?6
?4
?2
2
4
6
8
x
2
4
6
8
10
12
x
?2
?2
?4
?4
?6
?6
Find the intervals on which each function is continuous. You may use the provided graph to sketch the
function.
3) f ( x) =
{
2 x ? 10, x < 2
0,
4) f ( x) =
x¡Ý2
x2 ? x ? 2
x+1
f
f
?6
?4
4
4
2
2
?2
2
4
6
8
?8
10 x
?6
?4
?2
2
?2
?2
?4
?4
?6
?6
?8
?8
?10
?10
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-1-
4
6
x
Worksheet by Kuta Software LLC
Find the intervals on which each function is continuous.
x2
5) f ( x) =
2x + 4
6) f ( x) =
{
?
x 7
? ,
2 2
x¡Ü0
? x 2 + 2 x ? 2, x > 0
7) f ( x) = ?
x 2 ? x ? 12
x+3
8) f ( x) =
x2 ? x ? 6
x+2
Determine if each function is continuous. If the function is not continuous, find the x-axis location of and
classify each discontinuity.
9) f ( x) = ?
11) f ( x) =
x2
2x + 4
10) f ( x) =
x+1
x+1
x ?x?2
2
x2
x?1
12) f ( x) = ?
2
x +x+1
13)
f ( x) =
{
x 2 ? 4 x + 3, x ¡Ù 0
3,
x=0
14)
f ( x) =
?x2 , x ¡Ù 1
{
0,
x=1
Critical thinking questions:
15) Give an example of a function with
discontinuities at x = 1, 2, and 3.
?S c230F1B38 4Kouotdam mSgo9frtlw5aJrqe3 6LSLUCI.X z IAJlUlq YrGi2gQhhtPsg trVewsFe4r4vbe5dj.9 4 AMRaedZeR ywJidtQh9 GIRnOfPi1nyi4tYet rC4aKlNcYuxlNups9.b
16) Of the six basic trigonometric functions, which
are continuous over all real numbers? Which
are not? What types of discontinuities are
there?
-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Calculus
Name___________________________________
Continuity
Date________________ Period____
Find the intervals on which each function is continuous.
1) f ( x) =
{
x 2 + 2 x + 1, x < 1
x
? ,
2
2) f ( x) =
x¡Ý1
10
f
{
1, x ¡Ù 5
3, x = 5
f
8
8
6
6
4
4
2
2
?2
?6
?4
?2
2
4
6
8
x
2
4
6
8
10
12
x
?2
?2
?4
?4
?6
?6
(? ¡Þ, 5), (5, ¡Þ)
(? ¡Þ, 1), [1, ¡Þ)
Find the intervals on which each function is continuous. You may use the provided graph to sketch the
function.
3) f ( x) =
{
2 x ? 10, x < 2
0,
4) f ( x) =
x¡Ý2
x2 ? x ? 2
x+1
f
f
?6
?4
4
4
2
2
?2
2
4
6
8
?8
10 x
?6
?4
?2
2
?2
?2
?4
?4
?6
?6
?8
?8
?10
?10
6
x
(? ¡Þ, ?1), (?1, ¡Þ)
(? ¡Þ, 2), [2, ¡Þ)
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4
-1-
Worksheet by Kuta Software LLC
Find the intervals on which each function is continuous.
x2
5) f ( x) =
2x + 4
6) f ( x) =
{
?
x 7
? ,
2 2
x¡Ü0
? x 2 + 2 x ? 2, x > 0
(? ¡Þ, ?2), (?2, ¡Þ)
(? ¡Þ, 0], (0, ¡Þ)
7) f ( x) = ?
x 2 ? x ? 12
x+3
8) f ( x) =
(? ¡Þ, ?3), (?3, ¡Þ)
x2 ? x ? 6
x+2
(? ¡Þ, ?2), (?2, ¡Þ)
Determine if each function is continuous. If the function is not continuous, find the x-axis location of and
classify each discontinuity.
9) f ( x) = ?
x2
2x + 4
10) f ( x) =
Essential discontinuity at: x = ?2
11) f ( x) =
x+1
x+1
x ?x?2
2
Removable discontinuity at: x = ?1
Essential discontinuity at: x = 2
x2
x?1
12) f ( x) = ?
2
x +x+1
Essential discontinuity at: x = 1
Continuous
13)
f ( x) =
{
x 2 ? 4 x + 3, x ¡Ù 0
3,
x=0
14)
Continuous
f ( x) =
?x2 , x ¡Ù 1
{
0,
x=1
Removable discontinuity at: x = 1
Critical thinking questions:
15) Give an example of a function with
discontinuities at x = 1, 2, and 3.
Many answers.
1
( x ? 1)( x ? 2)( x ? 3)
16) Of the six basic trigonometric functions, which
are continuous over all real numbers? Which
are not? What types of discontinuities are
there?
Cont: sin, cos. Not cont: sec, csc, tan, cot. Essential.
Create your own worksheets like this one with Infinite Calculus. Free trial available at
?c z2v0H1k3e 7KVuUtraw nStoUfktsw5a3rbeV qL1LpCQ.f I 8ASldlz orAi2gyh6tks8 graensreCr0vCexds.2 B 8MBasdOeQ Xw7i9tOhB ZIvnzfMiQnSiDtne9 DCXaulDceuilHuosE.x
-2-
Worksheet by Kuta Software LLC
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