Worksheet: Domain and Range of a Function

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

Q1:

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}

Q2:

Using the figure below, determine the range of 𝑓(𝑥).

  • A[2,2]
  • B{0,4,3,2,1}
  • C{0,1,2,2,1}
  • D{0,1,2,4,3,2,1}
  • E[4,0]

Q3:

Given that 𝑓𝑋𝑌, 𝑋={9,6,5}, 𝑌={3,4,6,9}, and 𝑓={(9,4),(6,4),(5,9)}, which of the following sets correctly specify the range of the function?

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

Q4:

If 𝑓[2,21], where 𝑓(𝑥)=3𝑥10, find the range of 𝑓.

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

Q5:

Find the domain of the function 𝑓(𝑥)=𝑥.

  • A[0,)
  • B
  • C],0]
  • D(0,)

Q6:

Find the domain of the function 𝑓(𝑥)=32𝑥1.

  • A,12
  • B12,
  • C12,
  • D12
  • E12,

Q7:

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]

Q8:

Determine the domain of the function 𝑓(𝑥)=𝑥+4𝑥[4,4],8𝑥+40𝑥(4,5].ifif

  • A[0,8]
  • B{0,8}
  • C(4,5)
  • D[4,5]

Q9:

Determine the range of the function 𝑓(𝑥)=𝑥2𝑥<4,8𝑥4𝑥8.ifif

  • A{2,8}
  • B{2,4}
  • C{0,4}
  • D[2,4]
  • E(2,4]

Q10:

Determine the range of the function in the given figure.

  • A{5}
  • B{5}
  • C{5}
  • D{5}
  • E

Q11:

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

  • A[1,)
  • B{1}
  • C[4,)
  • D
  • E{4}

Q12:

Find the range of the function 𝑓(𝑥)=𝑥𝑥[0,3),3𝑥[3,5],8𝑥𝑥(5,8].ififif

  • A[0,8]
  • B{0,3}
  • C{0,8}
  • D{0,8}
  • E[0,3]

Q13:

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

  • A[33,33]
  • B[33,33]
  • C(33,33)
  • D(33,33)

Q14:

Determine the domain of the function 𝑓(𝑥)=𝑥+38𝑥.

  • A[3,8)
  • B[8,)
  • C(3,8)
  • D(,3]
  • E[3,8]

Q15:

Determine the domain of the function 𝑓(𝑥)=1|𝑥|65.

  • A{65,65}
  • B[65,65]
  • C[65,65]
  • D{65,65}

Q16:

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

  • A{𝑎,𝑐}
  • B{𝑎,𝑏,𝑐}
  • C{𝑏,𝑐}
  • D{𝑎,𝑏}

Q17:

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

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

Q18:

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

Evaluate 𝑓(2).

Evaluate 𝑓(3).

Evaluate 𝑓(0).

  • A3
  • B7
  • C1
  • D𝑓 is not defined at 0.
  • E2

What is the domain of 𝑓?

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

What is the range of 𝑓?

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

Solve 𝑓(𝑥)=3.

  • A𝑥=7 or 𝑥=3
  • B𝑥=2 or 𝑥=5
  • C𝑥=1 or 𝑥=3
  • D𝑥=3
  • E𝑥=1 or 𝑥=7

What is the solution set of 𝑓(𝑥)=1?

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

What is the solution set of 𝑓(𝑥)=0?

  • A𝜙
  • B{0}
  • C{1}
  • D{2}
  • E{7}

Q19:

Determine the domain and the range of the function 𝑓(𝑥)=6(𝑥+9)+8.

  • AThe domain is , and the range is .
  • BThe domain is {9}, and the range is {8}.
  • CThe domain is , and the range is (,8].
  • DThe domain is {8}, and the range is {9}.
  • EThe domain is (,8], and the range is .

Q20:

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+𝑚 elements, where 𝑛 = the size of the range of 𝑓 and 𝑚 = the size of the range of 𝑔.
  3. The range of 𝑓+𝑔 has at least 1 element.
  • Aa only
  • Ba and c
  • Cb only
  • Dc only

Q21:

What is the range of the function 𝑓(𝑥)=𝑥+12 on the domain (which is the domain of all of the integers)?

  • Aall the integers
  • Ball the numbers of the form𝑛2 where 𝑛 is an integer
  • CWe cannot tell the range because we do not know the codomain.
  • Dall the positive integers
  • Eall the rational numbers

Q22:

If 𝑓{4,1,4,2}[6,25] and 𝑓(𝑥)=𝑥+5, find the range of 𝑓.

  • A{1,9,3,4}
  • B{9,21,6}
  • C{9}
  • D{11}
  • E{1,3,3,13}

Q23:

If 𝑓, where 𝑓(𝑥)=𝑥+62, find the range of 𝑓.

  • A(,62)
  • B(,62]
  • C(62,)
  • D[62,)

Q24:

Given that 𝑋={𝑥𝑥,9𝑥10} and 𝑓𝑋:, where the graph of the function can be represented by 𝐺={(10,1),(7,1),(4,10),(1,10),(9,0)}, determine its range.

  • A{0,1,1,10}
  • B[9,10]
  • C{0,1,10,10,9,7,4,1}
  • D[10,1]
  • E{7,10,4,1,9}

Q25:

𝑋={14,7,11}, 𝑌={33,1,42,12,21}, and 𝑅 is a relation from 𝑋 to 𝑌, where 𝑎𝑅𝑏 means that 𝑎=13𝑏 for each 𝑎𝑋 and 𝑏𝑌. Determine the relation 𝑅, state whether it represents a function or not, and write its range if it is a function.

  • A𝑅={(14,42),(7,21)}, a function from 𝑋 to 𝑌, range ={42,21}
  • B𝑅={(14,42),(7,21),(11,33)}, a function from 𝑋 to 𝑌, range={42,21,33}
  • C𝑅={(14,42),(7,21),(11,33)}, not a function from 𝑋 to 𝑌
  • D𝑅={(14,42),(14,1),(7,21),(11,33)}, not a function from 𝑋 to 𝑌

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