Continuity Date Period

Kuta Software - Infinite Precalculus

Name___________________________________

Continuity

Date________________ Period____

Determine if each function is continuous at the given x-values. If not continuous, classify each

discontinuity.

1) f ( x)???

x

; at x = ?? and x = ?

x ????x

?

?

??

3) f ( x)???

5)

f ( x)???

??

??,

?

?

?

?

?

??

??

?

?

?

?

x

??

??

??

??

??

???

x ????x????

; at x = ??

x?

; at x = ??

x????

?

?

?

??

x

??

??

x????

; at x = ?

f(x)

??

??

?

x????

x????, x????

f(x)

?

??

{

2) f ( x) =

4) f ( x)???

x????

; at x = ?? and x = ?

x ? ????

6) f ( x) =

{

??x,

x????

?

?x ????x?????, x????

; at x = ?

Determine if each function is continuous. If the function is not continuous, find the x-axis

location of and classify each discontinuity.

7) f ( x)????

x

?

?x ????x????

8) f ( x)???

x

x ????x????

?

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9) f ( x)???

x ? ????x????

x????

11) f ( x) =

{

x????,

x?????

??x?????, x?????

10) f ( x)???

x

x ????x

12) f ( x)???

x????

x ? ????x

?

Find the intervals on which each function is continuous.

13) f ( x) =

{

15) f ( x)???

x????

?

x ????x????

x, x????

?, x????

17) f ( x)????x ? ????x????

19) f ( x)????

x????

x ? ???x

??,

14) f ( x) =

{

16) f ( x)???

x?

? ???x?????

?

18) f ( x)????

20) f ( x)???

x????

??x????, x????

x????

x ????x????

?

x

x ????x????

?

Critical thinking questions:

21) Write a function that has an infinite

discontinuity at x??????.

22) Write a function that is continuous over

(??, ?), (?, ?), and (?, ?) and

discontinuous everywhere else.

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Kuta Software - Infinite Precalculus

Name___________________________________

Continuity

Date________________ Period____

Determine if each function is continuous at the given x-values. If not continuous, classify each

discontinuity.

1) f ( x)???

x

; at x = ?? and x = ?

x ????x

?

?

??

??

?

?

?

?

??

??

?

?

?

x

??

??

??

??

??

???

x ????x????

; at x = ??

5)

x?

; at x = ??

x????

?

?

?

??

x

Continuous at x = ?

4) f ( x)???

x????

; at x = ?? and x = ?

x ? ????

Removable discontinuity at x = ??

Infinite discontinuity at x = ?

Continuous at x = ??

f ( x)???

?

??

??

x????

; at x = ?

f(x)

??

??

?

x????

x????, x????

?

Removable discontinuity at x = ?

Infinite discontinuity at x = ??

3) f ( x)???

??,

f(x)

?

??

{

2) f ( x) =

6) f ( x) =

Infinite discontinuity at x = ??

{

??x,

x????

?

?x ????x?????, x????

; at x = ?

Jump discontinuity at x = ?

Determine if each function is continuous. If the function is not continuous, find the x-axis

location of and classify each discontinuity.

7) f ( x)????

x

?

?x ????x????

8) f ( x)???

x

x ????x????

?

Infinite discontinuity at x = ??

Continuous

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9) f ( x)???

x ? ????x????

x????

10) f ( x)???

Removable discontinuity at x = ??

11) f ( x) =

{

x????,

x?????

??x?????, x?????

x

x ????x

?

Removable discontinuity at x = ?

Infinite discontinuity at x = ?

12) f ( x)???

x????

x ? ????x

Infinite discontinuities at x = ??, x = ?

Jump discontinuity at x = ??

Find the intervals on which each function is continuous.

13) f ( x) =

{

x, x????

?, x????

14) f ( x) =

(??, ?), (?, ?)

15) f ( x)???

x????

?

x ????x????

x????

??x????, x????

(??, ?), [?, ?)

16) f ( x)???

x?

? ???x?????

?

(??, ?)

(??, ?), (?, ?), (?, ?)

17) f ( x)????x ? ????x????

{

??,

18) f ( x)????

(??, ?)

x????

x ????x????

?

(??, ?), (?, ?), (?, ?)

19) f ( x)????

x????

x ? ???x

20) f ( x)???

(??, ?), (?, ?), (?, ?)

x

x ????x????

?

(??, ?), (?, ?)

Critical thinking questions:

21) Write a function that has an infinite

discontinuity at x??????.

f ( x)???

?

x??????

22) Write a function that is continuous over

(??, ?), (?, ?), and (?, ?) and

discontinuous everywhere else.

f ( x)???

x????

x ? ???x

Create your own worksheets like this one with Infinite Precalculus. Free trial available at

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