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Worksheet: Domain and Range of a Function

Q1:

Determine the range of 𝑓 ( π‘₯ ) .

  • A { βˆ’ 8 , 1 4 , βˆ’ 2 }
  • B { 1 6 , 1 8 , βˆ’ 2 0 , βˆ’ 4 , 1 5 }
  • C { βˆ’ 2 0 , 1 4 , 1 5 , 1 6 , 1 8 , βˆ’ 8 , βˆ’ 4 , βˆ’ 2 }
  • D { βˆ’ 2 0 , βˆ’ 4 }
  • E { 1 6 , 1 8 , 1 5 }

Q2:

Given that 𝑓 ∢ 𝑋 β†’ π‘Œ , 𝑋 = { βˆ’ 9 , βˆ’ 6 , βˆ’ 5 } , π‘Œ = { 3 , 4 , 6 , 9 } , and 𝑓 = { ( βˆ’ 9 , 4 ) , ( βˆ’ 6 , 4 ) , ( βˆ’ 5 , 9 ) } , which of the following sets correctly specify the range of the function?

  • A { ( βˆ’ 9 , 4 ) , ( βˆ’ 6 , 4 ) , ( βˆ’ 5 , 9 ) }
  • B { 3 , 4 , 6 , 9 }
  • C { 4 , 4 , 9 }
  • D { 4 , 9 }
  • E { βˆ’ 9 , βˆ’ 6 , βˆ’ 5 }

Q3:

Find the domain of the function .

  • A
  • B
  • C
  • D

Q4:

Find the range of the function

  • A
  • B
  • C
  • D
  • E

Q5:

Given the function 𝑓 = { ( 2 , 1 ) , ( 1 , 3 ) , ( 3 , βˆ’ 1 ) , ( 7 , 3 ) } , answer the following.

Evaluate 𝑓 ( 2 ) .

Evaluate 𝑓 ( 3 ) .

Evaluate 𝑓 ( 0 ) .

  • A2
  • B1
  • C 𝑓 is not defined at 0.
  • D3
  • E7

What is the domain of 𝑓 ?

  • A { 1 , 2 , 3 , 7 }
  • B { βˆ’ 1 , 1 , 3 }
  • C { 1 , 3 , 7 }
  • D { 1 , 2 , 3 }
  • E { 0 , 1 , 2 , 3 }

What is the range of 𝑓 ?

  • A { 1 , 2 , 3 , 7 }
  • B { βˆ’ 1 , 1 , 2 }
  • C { 0 , βˆ’ 1 , 1 , 3 }
  • D { βˆ’ 1 , 1 , 3 }
  • E { 0 , 1 , 2 , 3 }

Solve 𝑓 ( π‘₯ ) = 3 .

  • A π‘₯ = 3
  • B π‘₯ = βˆ’ 1 or π‘₯ = 3
  • C π‘₯ = 2 or π‘₯ = 5
  • D π‘₯ = 1 or π‘₯ = 7
  • E π‘₯ = 7 or π‘₯ = 3

What is the solution set of 𝑓 ( π‘₯ ) = βˆ’ 1 ?

  • A { 7 }
  • B { 3 }
  • C { βˆ’ 1 }
  • D { 2 }
  • E { 1 }

What is the solution set of 𝑓 ( π‘₯ ) = 0 ?

  • A { 0 }
  • B { 7 }
  • C { 2 }
  • D { }
  • E { βˆ’ 1 }

Q6:

Determine the range of the function represented by the figure in 𝑋 .

  • A { βˆ’ 5 , βˆ’ 4 }
  • B { βˆ’ 5 , βˆ’ 4 , βˆ’ 3 , βˆ’ 2 }
  • C { βˆ’ 5 , βˆ’ 2 }
  • D { βˆ’ 5 , βˆ’ 4 , βˆ’ 3 }
  • E { βˆ’ 3 }

Q7:

Determine the range of the function represented by the figure in 𝑋 .

  • A { 3 , 4 }
  • B { 3 , 4 , 5 , 6 }
  • C { 3 , 6 }
  • D { 4 , 5 }
  • E { 5 }

Q8:

Determine the range of the function represented by the figure in 𝑋 .

  • A { βˆ’ 8 , βˆ’ 7 }
  • B { βˆ’ 8 , βˆ’ 7 , βˆ’ 6 , βˆ’ 5 }
  • C { βˆ’ 8 , βˆ’ 5 }
  • D { βˆ’ 7 , βˆ’ 6 , βˆ’ 5 }
  • E { βˆ’ 5 }

Q9:

Determine the domain of the function

  • A
  • B
  • C
  • D

Q10:

Determine the domain of the function

  • A
  • B
  • C
  • D

Q11:

If , where , find the range of .

  • A
  • B
  • C
  • D

Q12:

Determine the range of the function in the given figure.

  • A ℝ βˆ’ { βˆ’ 5 }
  • B { 5 }
  • C ℝ
  • D { βˆ’ 5 }
  • E ℝ βˆ’ { 5 }

Q13:

Determine the domain and the range of the function .

  • A The domain is , and the range is .
  • B The domain is , and the range is .
  • C The domain is , and the range is .
  • D The domain is , and the range is .
  • E The domain is , and the range is .

Q14:

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

  1. The range of 𝑓 + 𝑔 has at most 4 elements.
  2. The range of 𝑓 + 𝑔 has 𝑛 + π‘š elements, where 𝑛 = the size of the range of 𝑓 and π‘š = the size of the range of 𝑔 .
  3. The range of 𝑓 + 𝑔 has at least 1 element.
  • A c only
  • B a only
  • C b only
  • D a and c

Q15:

Determine the range of the function

  • A
  • B
  • C
  • D
  • E

Q16:

Using the figure below, determine the range of .

  • A
  • B
  • C
  • D
  • E

Q17:

Find the domain of the function .

  • A
  • B
  • C
  • D
  • E

Q18:

Determine the domain of the function represented in the graph below.

  • A
  • B
  • C
  • D
  • E

Q19:

Determine the domain of the function .

  • A
  • B
  • C
  • D

Q20:

The figure below shows the graph of a function 𝑓 .

What is the range of the function?

  • A { βˆ’ 3 , βˆ’ 2 , βˆ’ 1 , 0 , 1 }
  • B { βˆ’ 3 , βˆ’ 2 , βˆ’ 1 , 0 }
  • C the interval [ βˆ’ 3 , 0 ]
  • D { βˆ’ 3 , βˆ’ 2 , 0 }
  • EIt is not possible to determine the range.

Q21:

Determine the domain of the function .

  • A
  • B
  • C
  • D
  • E

Q22:

Determine the range of the function represented in the figure below.

  • A { π‘Ž , 𝑐 }
  • B { π‘Ž , 𝑏 }
  • C { 𝑏 , 𝑐 }
  • D { π‘Ž , 𝑏 , 𝑐 }

Q23:

Determine the range of the function represented in the figure below.

  • A { π‘Ž , 𝑐 }
  • B { π‘Ž , 𝑏 }
  • C { 𝑏 , 𝑐 }
  • D { π‘Ž }
  • E { π‘Ž , 𝑏 , 𝑐 }

Q24:

Determine the range of the function represented in the figure below.

  • A { π‘Ž , 𝑐 }
  • B { π‘Ž , 𝑏 }
  • C { π‘Ž , 𝑏 , 𝑐 }
  • D { 𝑏 , 𝑐 }

Q25:

Determine the domain of the function .

  • A
  • B
  • C
  • D