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.

  • Aℝ−{0}
  • Bℝ−[−7,7]
  • Cℝ−{7,−7}
  • D{7,−7}
  • Eℝ

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.

  • Aℝ−{0}
  • Bℝ
  • C{−4,4}
  • Dℝ−{−4}

Q7:

Determine the domain of the function in the given figure.

  • A{−6}
  • Bℝ
  • Cℝ−{−6}
  • Dℝ−{0}
  • Eℝ−{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.

  • Aℝ−{−9,6}
  • B{−9,3}
  • Cℝ−{−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.

  • A{−8}
  • Bℝ
  • Cℝ−{−8}
  • Dℝ−{0}
  • Eℝ−{8}

Q16:

Determine the domain of the function in the given figure.

  • Aℝ−{−4}
  • Bℝ−{−5}
  • Cℝ−{0}
  • Dℝ
  • Eℝ−{−5,−4}

Q17:

The domain of the function 𝑓(𝑥) is .

  • A{−5,−4,−3,−2,−1}
  • B[−5,−1]
  • C{−8,−7,−6,−5,−9}
  • D{−9,−8,−7,−6,−5,−4,−3,−2,−1}
  • E[−9,−5]

Q18:

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−{2}.
  • EThe domain is ℝ−{2}, and the range is ℝ−{0}.

Q19:

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}.

Q20:

Determine the range of the following function.

  • Aℝ−{0}
  • Bℝ−[−1,1]
  • Cℝ−{−1,1}
  • D{−1,1}
  • Eℝ

Q21:

Find the domain and the range of 𝑓(𝑥)=4−3𝑥, and discuss its monotony.

  • AThe domain is ℝ−43, the range is 43, and the function is decreasing over its domain.
  • BThe domain is ℝ, the range is ℝ, and the function is decreasing over its domain.
  • CThe domain is ℝ, the range is ℝ, and the function is increasing over its domain.
  • DThe domain is ℝ−43, the range is 43, and the function is increasing over its domain.
  • EThe domain is ℝ−43,4, the range is 43,4, and the function is decreasing over its domain.

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