# Lesson Worksheet: Domain and Range of a Function Mathematics

In this worksheet, we will practice identifying the domain and range of functions from their equations.

Q1:

Determine the range of . • A
• B
• C
• D
• E

Q2:

Using the figure below, determine the range of . • A
• B
• C
• D
• E

Q3:

Given that , , , and , which of the following sets correctly specify the range of the function?

• A
• B
• C
• D
• E

Q4:

If , where , find the range of .

• A
• B
• C
• D

Q5:

Find the domain of the function .

• A
• B
• C
• D

Q6:

The figure below shows the graph of a function . What is the range of the function?

• A
• B
• CIt is not possible to determine the range.
• D
• Ethe interval

Q7:

Determine the range of the function in the given figure. • A
• B
• C
• D
• E

Q8:

Determine the domain of the function represented in the graph below. • A
• B
• C
• D
• E

Q9:

Determine the domain of the function .

• A
• B
• C
• D

Q10:

Determine the domain of the function .

• A
• B
• C
• D
• E

Q11:

Determine the range of the function represented in the figure below. • A
• B
• C
• D

Q12:

Determine the range of the function represented by the figure in . • A
• B
• C
• D
• E

Q13:

Given the function , answer the following.

Evaluate .

Evaluate .

Evaluate .

• A3
• B7
• C1
• D is not defined at 0.
• E2

What is the domain of ?

• A
• B
• C
• D
• E

What is the range of ?

• A
• B
• C
• D
• E

Solve .

• A or
• B or
• C or
• D
• E or

What is the solution set of ?

• A
• B
• C
• D
• E

What is the solution set of ?

• A
• B
• C
• D
• E

Q14:

Determine the domain and the range of the function .

• AThe domain is , and the range is .
• BThe domain is , and the range is .
• CThe domain is , and the range is .
• DThe domain is , and the range is .
• EThe domain is , and the range is .

Q15:

Functions and have the same domain {1, 2, 3, 4}. Which of the following statements must be true?

1. The range of has at most 4 elements.
2. The range of has elements, where = the size of the range of and = the size of the range of .
3. The range of has at least 1 element.
• Aa only
• Ba and c
• Cb only
• Dc only

Q16:

What is the range of the function on the domain (which is the domain of all of the integers)?

• Aall the integers
• Ball the numbers of the form where is an integer
• CWe cannot tell the range because we do not know the codomain.
• Dall the positive integers
• Eall the rational numbers

Q17:

If and , find the range of .

• A
• B
• C
• D
• E

Q18:

If , where , find the range of .

• A
• B
• C
• D

Q19:

Given that and , where the graph of the function can be represented by , determine its range.

• A
• B
• C
• D
• E

Q20:

, , and is a relation from to , where means that for each and . Determine the relation , state whether it represents a function or not, and write its range if it is a function.

• A, a function from to , range
• B, a function from to , range
• C, not a function from to
• D, not a function from to

Q21:

For two sets and , a function exists from to . Also, , , and means is a multiple of . If , , and , find the range of the function.

• A
• B
• C
• D
• E

Q22:

If is a function from the set to the set , which set contains the range of ?

• A
• B

Q23:

is a function from to , where means that is divisible by for each and . If , , and , determine the range of the function.

• A
• B
• C
• D

Q24:

, , is the set of natural numbers, and is a function from to where means . Given that and , write the range of the function.

• A
• B
• C
• D

Q25:

If , where , find the range of .

• A
• B
• C
• D
• E