# Worksheet: Continuity of a Function

Q1:

Find the set on which is continuous.

• A
• B
• C
• D

Q2:

Find the set on which is continuous.

• A is continuous on .
• B is continuous on .
• C is continuous on .
• D is continuous on .

Q3:

Use continuity to evaluate .

• A9
• B1
• C
• D3
• E0

Q4:

The function is given by Determine and so that is continuous everywhere.

• A,
• B,
• C,
• D,

Q5:

Find the set on which is continuous.

• AThe function is continuous on because and are continuous on .
• BThe function is continuous on .
• CThe function is continuous on .
• DThe function is continuous on .
• EThe function is continuous on .

Q6:

Given that and are continuous functions such that and , determine .

• A
• B
• C
• D
• E

Q7:

Which of the following holds for ?

• AThe function is continuous on .
• BThe function is continuous on .
• CThe function is continuous on because both of and are continuous on .
• DThe function is continuous on because is continuous on .
• EThe function is continuous on because is continuous on .

Q8:

Use continuity to evaluate .

• A8
• B
• C
• D
• E

Q9:

Use continuity to evaluate .

Q10:

Use continuity to evaluate .

• A1
• B0
• C
• D

Q11:

Given that and are continuous functions such that and , determine .

• A
• B
• C
• D
• E

Q12:

Find the set on which is continuous.

• A is continuous on .
• B is continuous on .
• C is continuous on .
• D is continuous on .
• E is continuous on .

Q13:

Determine the value of that makes the function continuous at , given

• A1
• B
• C
• D

Q14:

Suppose and What can be said of the continuity of at ?

• AThe function is discontinuous at because is undefined.
• BThe function is discontinuous at because .
• CThe function is discontinuous at because does not exist.
• DThe function is continuous at .

Q15:

Suppose What can be said of the continuity of at ?

• AThe function is discontinuous at because .
• BThe function is discontinuous at because is undefined.
• CThe function is continuous at .
• DThe function is discontinuous at because does not exist.
• EThe function is continuous on .

Q16:

Given , if possible or necessary, define so that is continuous at .

• AThe function cannot be made continuous at because is undefined.
• B makes continuous at .
• CNo value of will make continuous because does not exist.
• DThe function is already continuous at .

Q17:

Suppose Discuss whether it is possible to define to obtain a function that is continuous at this point.

• AThe function cannot be defined to be continuous at because is undefined.
• BThe function cannot be defined to be continuous at because does not exist.
• CThe function can be defined to be continuous at as
• DThe function is continuous at .
• EThe function can be defined to be continuous at as