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

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-2-

Worksheet by Kuta Software LLC

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