Worksheet: Finding the Domain and Range of a Function Graphically

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In this worksheet, we will practice working with the concepts of the domain and range of a function and identifying them from their graphs.

Q1:

The domain of the function is .

  • A
  • B
  • C
  • D
  • E

Q2:

Find the domain and the range of the function 𝑓 ( 𝑥 ) = ( 𝑥 + 1 ) − 2 .

  • A The domain is ℝ − { − 1 } and the range is ℝ − { − 2 } .
  • B The domain is [ − 2 , ∞ ) and the range is ℝ .
  • C The domain is ℝ − { − 2 } and the range is ℝ − { − 1 } .
  • D The domain is ℝ and the range is [ − 2 , ∞ ) .

Q3:

Determine the domain and the range of the function represented in the shown figure.

  • AThe domain is ℝ − { 3 } , and the range is ℝ − { 4 } .
  • BThe domain is ℝ − { − 4 } , and the range is ℝ − { 3 } .
  • CThe domain is ℝ − { 4 } , and the range is ℝ − { − 3 } .
  • DThe domain is ℝ − { − 3 } , and the range is ℝ − { − 4 } .
  • EThe domain is ℝ − { − 4 } , and the range is ℝ − { − 3 } .

Q4:

Determine the range of the following function.

  • A ℝ − { 7 , − 7 }
  • B ℝ − { 0 }
  • C ℝ
  • D { 7 , − 7 }
  • E ℝ − [ − 7 , 7 ]

Q5:

Find the domain and range of the function 𝑓 ( 𝑥 ) = − 1 𝑥 − 5 .

  • A The domain is { 5 } and the range is ℝ .
  • B The domain is ℝ and the range is ℝ .
  • C The domain is ℝ and the range is { 5 } .
  • D The domain is ℝ − { 5 } and the range is ℝ − { 0 } .

Q6:

Determine the domain of the following function.

  • A ℝ − { − 4 }
  • B ℝ − { 0 }
  • C { − 4 , 4 }
  • D ℝ

Q7:

Determine the domain of the function in the given figure.

  • A ℝ − { − 6 }
  • B ℝ − { 0 }
  • C { − 6 }
  • D ℝ
  • E ℝ − { 6 }

Q8:

Determine the domain and the range of the function 𝑓 ( 𝑥 ) = − 4 .

  • A The domain is ℝ − { 0 } and the range is { 0 , − 4 } .
  • B The domain is { − 4 } and the range is ℝ .
  • C The domain is { 0 , − 4 } and the range is ℝ − { 0 } .
  • D The domain is ℝ and the range is { − 4 } .

Q9:

Determine the domain and the range of the function represented by the shown graph.

  • A The domain is ℝ − { − 4 } , and the range is ℝ − { 0 } .
  • B The domain is ( − ∞ , 0 ] , and the range is ℝ .
  • C The domain is ℝ − { 0 } , and the range is ℝ − { − 4 } .
  • D The domain is ℝ , and the range is ℝ .
  • E The domain is ℝ , and the range is ( − ∞ , 0 ] .

Q10:

Find the domain and the range of the function 𝑓 ( 𝑥 ) = ( 𝑥 − 1 ) in ℝ .

  • A The domain is ℝ − { 1 } , and the range is ℝ − { 0 } .
  • B The domain is [ 0 , ∞ ) , and the range is ℝ .
  • C The domain is ℝ − { 0 } , and the range is ℝ − { 1 } .
  • D The domain is ℝ , and the range is ℝ .

Q11:

Determine the domain of the function represented by the following graph.

  • A ℝ − { − 9 , 3 }
  • B ℝ − { − 9 , 6 }
  • C [ − 9 , 3 ]
  • D [ − 9 , 6 ]
  • E { − 9 , 3 }

Q12:

The figure below shows the graph of a function .

What is the domain of the function?

  • A the set of real numbers between 1 and 4
  • B
  • C It is not possible to determine the domain.
  • D
  • Ethe interval

Q13:

Find the domain and the range of the function 𝑓 ( 𝑥 ) = 2 ( 𝑥 + 7 ) − 1 .

  • A The domain is ℝ − { − 7 } and the range is ℝ − { − 1 } .
  • B The domain is [ − 1 , ∞ ) and the range is ℝ .
  • C The domain is ℝ − { − 1 } and the range is ℝ − { − 7 } .
  • D The domain is ℝ and the range is [ − 1 , ∞ ) .

Q14:

Determine the domain and the range of the function represented in the shown figure.

  • AThe domain is ℝ − { − 4 } , and the range is ℝ − { 1 } .
  • BThe domain is ℝ − { − 1 } , and the range is ℝ − { − 4 } .
  • CThe domain is ℝ − { 1 } , and the range is ℝ − { 4 } .
  • DThe domain is ℝ − { 4 } , and the range is ℝ − { − 1 } .
  • EThe domain is ℝ − { − 1 } , and the range is ℝ − { 4 } .

Q15:

Determine the domain of the function in the given figure.