Lesson Worksheet: Domain and Range of a Function Mathematics • 9th Grade

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

Q1:

𝑋 and 𝑌 are two sets of number where 𝑋={10,1,2,8} and 𝑌={12,7,60,6,48,4}. The function 𝑓(𝑥)=6𝑥 where 𝑓∶𝑋⟶𝑌. Find the ordered pairs that satisfy the function and its range.

  • A𝑓={(−60,10),(−6,1),(−12,2),(−48,8)}, range ={10,1,2,8}
  • B𝑓={(60,10),(6,1),(12,2),(48,8)}, range ={10,1,2,8}
  • C𝑓={(10,−60),(1,−6),(2,−12),(8,−48)}, range ={−60,−6,−12,−48}
  • D𝑓={(10,60),(1,6),(2,12),(8,48)}, range ={60,6,12,48}

Q2:

What is the range of the function 𝑓(𝑥)=3𝑥−1, if 𝑓’s domain is {−2,−1,0,1,2}?

  • A{−1,2,11}
  • B𝑅
  • C{0,1,2}
  • D{−1,2,35}

Q3:

Determine the range of 𝑓(𝑥).

  • A{−8,14,−2}
  • B{−20,14,15,16,18,−8,−4,−2}
  • C{−20,−4}
  • D{16,18,15}
  • E{16,18,−20,−4,15}

Q4:

The figure below shows the graph of a function 𝑓.

What is the range of the function?

  • A{−3,−2,0}
  • B{−3,−2,−1,0}
  • CIt is not possible to determine the range.
  • D{−3,−2,−1,0,1}
  • Ethe interval [−3,0]

Q5:

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

  • A[1,∞)
  • Bℝ−{1}
  • C[4,∞)
  • Dℝ
  • Eℝ−{4}

Q6:

Determine the range of the function represented by the graph below.

  • A[1,∞[
  • B]−∞,−7]
  • C[−7,∞[
  • D]−∞,1]
  • E]1,∞[

Q7:

Determine the domain and the range of the function 𝑓(𝑥)=𝑥+1.

  • AThe domain of 𝑓 is (1,∞) and the range is ℝ.
  • BThe domain of 𝑓 is ℝ and the range is ℝ.
  • CThe domain of 𝑓 is ℝ and the range is [1,∞).
  • DThe domain of 𝑓 is ℝ and the range is (1,∞).
  • EThe domain of 𝑓 is [1,∞) and the range is ℝ.

Q8:

Find the domain of the function 𝑓(𝑥)=√𝑥+2.

  • Aℝ
  • B[2,∞)
  • C(−2,∞)
  • D[−2,∞)
  • E(2,∞)

Q9:

If 𝑓∶[2,21]⟶ℝ, where 𝑓(𝑥)=3𝑥−10, find the range of 𝑓.

  • A[16,73)
  • B[16,73]
  • C[−4,53]
  • D[−4,53)

Q10:

Determine the domain of the function 𝑓(𝑥)=√|𝑥|−33.

  • A[−33,33]
  • Bℝ−[−33,33]
  • Cℝ−(−33,33)
  • D(−33,33)

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