Worksheet: Domain and Range from Function Graphs

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

Q1:

The domain of the function 𝑓(𝑥) is .

  • A { − 7 , − 6 , − 5 , − 4 , − 3 }
  • B [ − 7 , − 3 ]
  • C { 1 , 2 , 3 , 4 , 5 }
  • D { 1 , 2 , 3 , 4 , 5 , − 7 , − 6 , − 5 , − 4 , − 3 }
  • E [ 1 , 5 ]

Q2:

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

  • AThe domain is ℝ−{−2} and the range is ℝ−{−1}.
  • BThe domain is ℝ and the range is [−2,∞).
  • CThe domain is ℝ−{−1} and the range is ℝ−{−2}.
  • DThe domain is [−2,∞) and the range is ℝ.

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

Q4:

Determine the range of the following function.

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

Q5:

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

  • AThe domain is ℝ and the range is {5}.
  • BThe domain is ℝ−{5} and the range is ℝ−{0}.
  • CThe domain is ℝ and the range is ℝ.
  • DThe domain is {5} and the range is ℝ.

Q6:

Determine the domain of the following function.

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

Q7:

Determine the domain of the function in the given figure.

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

Q8:

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

  • AThe domain is ℝ and the range is {−4}.
  • BThe domain is {0,−4} and the range is ℝ−{0}.
  • CThe domain is {−4} and the range is ℝ.
  • DThe domain is ℝ−{0} and the range is {0,−4}.

Q9:

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

  • AThe domain is (−∞,0], and the range is ℝ.
  • BThe domain is ℝ, and the range is ℝ.
  • CThe domain is ℝ, and the range is (−∞,0].
  • DThe domain is ℝ−{0}, and the range is ℝ−{−4}.
  • EThe domain is ℝ−{−4}, and the range is ℝ−{0}.

Q10:

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

  • AThe domain is [0,∞), and the range is ℝ.
  • BThe domain is ℝ−{0}, and the range is ℝ−{1}.
  • CThe domain is ℝ−{1}, and the range is ℝ−{0}.
  • DThe domain is ℝ, and the range is ℝ.

Q11:

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

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

Q12:

The figure below shows the graph of a function 𝑓.

What is the domain of the function?

  • Athe set of real numbers between 1 and 4
  • B { 1 , 2 , 3 , 4 }
  • CIt is not possible to determine the domain.
  • Dthe interval [1,4]
  • E { 1 , 2 , 3 , 4 , 5 }

Q13:

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

  • AThe domain is ℝ−{−1} and the range is ℝ−{−7}.
  • BThe domain is ℝ and the range is [−1,∞).
  • CThe domain is ℝ−{−7} and the range is ℝ−{−1}.
  • DThe domain is [−1,∞) and the range is ℝ.

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

Q15:

Determine the domain of the function in the given figure.