Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Lesson: Domain and Range of a Function

Video

04:29

Sample Question Videos

Worksheet • 25 Questions • 3 Videos

Q1:

Determine the range of 𝑓 ( π‘₯ ) .

  • A { βˆ’ 2 0 , βˆ’ 4 }
  • B { 1 6 , 1 8 , 1 5 }
  • C { 1 6 , 1 8 , βˆ’ 2 0 , βˆ’ 4 , 1 5 }
  • D { βˆ’ 2 0 , 1 4 , 1 5 , 1 6 , 1 8 , βˆ’ 8 , βˆ’ 4 , βˆ’ 2 }
  • E { βˆ’ 8 , 1 4 , βˆ’ 2 }

Q2:

Using the figure below, determine the range of 𝑓 ( π‘₯ ) .

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

Q3:

Given that 𝑓 ∢ 𝑋 β†’ π‘Œ , 𝑋 = { βˆ’ 9 , βˆ’ 6 , βˆ’ 5 } , π‘Œ = { 3 , 4 , 6 , 9 } , and 𝑓 = { ( βˆ’ 9 , 4 ) , ( βˆ’ 6 , 4 ) , ( βˆ’ 5 , 9 ) } , which of the following sets correctly specify the range of the function?

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

Q4:

If 𝑓 ∢ [ 2 , 2 1 ] ⟢ ℝ , where 𝑓 ( π‘₯ ) = 3 π‘₯ βˆ’ 1 0 , find the range of 𝑓 .

  • A [ βˆ’ 4 , 5 3 ]
  • B [ 1 6 , 7 3 [
  • C [ βˆ’ 4 , 5 3 [
  • D [ 1 6 , 7 3 ]

Q5:

Find the domain of the function 𝑓 ( π‘₯ ) = √ π‘₯ .

  • A [ 0 , ∞ [
  • B ℝ
  • C ] βˆ’ ∞ , 0 ]
  • D ] 0 , ∞ [

Q6:

Find the domain of the function 𝑓 ( π‘₯ ) = βˆ’ 3 √ 2 π‘₯ βˆ’ 1 .

  • A  1 2 , ∞ 
  • B ℝ βˆ’  1 2 
  • C  βˆ’ ∞ , 1 2 
  • D  βˆ’ 1 2 , ∞ 
  • E ℝ βˆ’  1 2 , ∞ 

Q7:

The figure below shows the graph of a function .

What is the range of the function?

  • A
  • BIt is not possible to determine the range.
  • C
  • D the interval
  • E

Q8:

Determine the domain of the function

  • A [ βˆ’ 4 , 5 ]
  • B [ 0 , 8 ]
  • C ] βˆ’ 4 , 5 [
  • D { 0 , 8 }

Q9:

Determine the range of the function

  • A [ βˆ’ 2 , 4 ]
  • B { βˆ’ 2 , 8 }
  • C ℝ βˆ’ { 0 , 4 }
  • D ] βˆ’ 2 , 4 ]
  • E ℝ βˆ’ { βˆ’ 2 , 4 }

Q10:

Determine the range of the function in the given figure.

  • A { βˆ’ 5 }
  • B ℝ βˆ’ { 5 }
  • C { 5 }
  • D ℝ
  • E ℝ βˆ’ { βˆ’ 5 }

Q11:

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

  • A [ 4 , ∞ [
  • B ℝ
  • C [ 1 , ∞ [
  • D ℝ βˆ’ { 1 }
  • E ℝ βˆ’ { 4 }

Q12:

Find the range of the function

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

Q13:

Determine the domain of the function 𝑓 ( π‘₯ ) = √ | π‘₯ | βˆ’ 3 3 .

  • A ℝ βˆ’ ] βˆ’ 3 3 , 3 3 [
  • B ] βˆ’ 3 3 , 3 3 [
  • C [ βˆ’ 3 3 , 3 3 ]
  • D ℝ βˆ’ [ βˆ’ 3 3 , 3 3 ]

Q14:

Determine the domain of the function 𝑓 ( π‘₯ ) = √ π‘₯ + 3 βˆ’ √ 8 βˆ’ π‘₯ .

  • A [ βˆ’ 3 , 8 ]
  • B ] βˆ’ ∞ , βˆ’ 3 ]
  • C ] βˆ’ 3 , 8 [
  • D [ 8 , ∞ [
  • E [ βˆ’ 3 , 8 [

Q15:

Determine the domain of the function 𝑓 ( π‘₯ ) = 1 | π‘₯ | βˆ’ 6 5 .

  • A ℝ βˆ’ { βˆ’ 6 5 , 6 5 }
  • B { βˆ’ 6 5 , 6 5 }
  • C ℝ βˆ’ [ βˆ’ 6 5 , 6 5 ]
  • D [ βˆ’ 6 5 , 6 5 ]

Q16:

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

  • A { π‘Ž , 𝑏 , 𝑐 }
  • B { π‘Ž , 𝑏 }
  • C { 𝑏 , 𝑐 }
  • D { π‘Ž , 𝑐 }

Q17:

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

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

Q18:

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

Evaluate 𝑓 ( 2 ) .

Evaluate 𝑓 ( 3 ) .

Evaluate 𝑓 ( 0 ) .

  • A 𝑓 is not defined at 0.
  • B2
  • C1
  • D7
  • E3

What is the domain of 𝑓 ?

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

What is the range of 𝑓 ?

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

Solve 𝑓 ( π‘₯ ) = 3 .

  • A π‘₯ = 1 or π‘₯ = 7
  • B π‘₯ = βˆ’ 1 or π‘₯ = 3
  • C π‘₯ = 2 or π‘₯ = 5
  • D π‘₯ = 7 or π‘₯ = 3
  • E π‘₯ = 3

What is the solution set of 𝑓 ( π‘₯ ) = βˆ’ 1 ?

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

What is the solution set of 𝑓 ( π‘₯ ) = 0 ?

  • A { }
  • B { 7 }
  • C { βˆ’ 1 }
  • D { 2 }
  • E { 0 }

Q19:

Determine the domain and the range of the function 𝑓 ( π‘₯ ) = βˆ’ 6 ( π‘₯ + 9 ) + 8 3 .

  • A The domain is ℝ , and the range is ℝ .
  • B The domain is ℝ , and the range is ] βˆ’ ∞ , 8 ] .
  • C The domain is ] βˆ’ ∞ , 8 ] , and the range is ℝ .
  • D The domain is ℝ βˆ’ { 8 } , and the range is ℝ βˆ’ { βˆ’ 9 } .
  • E The domain is ℝ βˆ’ { βˆ’ 9 } , and the range is ℝ βˆ’ { 8 } .

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 + π‘š elements, where 𝑛 = the size of the range of 𝑓 and π‘š = the size of the range of 𝑔 .
  3. The range of 𝑓 + 𝑔 has at least 1 element.
  • A a and c
  • B a only
  • C b only
  • D c only

Q21:

What is the range of the function 𝑓 ( π‘₯ ) = π‘₯ + 1 2 on the domain β„€ (which is the domain of all of the integers)?

  • Aall the numbers of the form 𝑛 2 where 𝑛 is an integer
  • Ball the rational numbers
  • CWe cannot tell the range because we do not know the codomain.
  • Dall the positive integers
  • Eall the integers

Q22:

If 𝑓 ∢ { βˆ’ 4 , βˆ’ 1 , 4 , βˆ’ 2 } β†’ [ 6 , 2 5 ] and 𝑓 ( π‘₯ ) = π‘₯ + 5 2 , find the range of 𝑓 .

  • A { 9 , 2 1 , 6 }
  • B { 1 1 }
  • C { 1 , 3 , βˆ’ 3 , 1 3 }
  • D { 1 , 9 , 3 , 4 }
  • E { 9 }

Q23:

If , where , find the range of .

  • A
  • B
  • C
  • D

Q24:

Given that 𝑋 = { π‘₯ ∢ π‘₯ ∈ β„€ , βˆ’ 9 ≀ π‘₯ ≀ 1 0 } and 𝑓 𝑋 β†’ ℝ : , where the graph of the function can be represented by 𝐺 = { ( 1 0 , 1 ) , ( βˆ’ 7 , βˆ’ 1 ) , ( βˆ’ 4 , βˆ’ 1 0 ) , ( βˆ’ 1 , βˆ’ 1 0 ) , ( βˆ’ 9 , 0 ) } 𝑓 , determine its range.

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

Q25:

𝑋 = { 1 4 , 7 , 1 1 } , π‘Œ = { 3 3 , 1 , 4 2 , 1 2 , 2 1 } , and 𝑅 is a relation from 𝑋 to π‘Œ , where π‘Ž 𝑅 𝑏 means that π‘Ž = 1 3 𝑏 for each π‘Ž ∈ 𝑋 and 𝑏 ∈ π‘Œ . Determine the relation 𝑅 , state whether it represents a function or not, and write its range if it is a function.

  • A 𝑅 = { ( 1 4 , 4 2 ) , ( 7 , 2 1 ) , ( 1 1 , 3 3 ) } , a function from 𝑋 to π‘Œ , range = { 4 2 , 2 1 , 3 3 }
  • B 𝑅 = { ( 1 4 , 4 2 ) , ( 1 4 , 1 ) , ( 7 , 2 1 ) , ( 1 1 , 3 3 ) } , not a function from 𝑋 to π‘Œ
  • C 𝑅 = { ( 1 4 , 4 2 ) , ( 7 , 2 1 ) , ( 1 1 , 3 3 ) } , not a function from 𝑋 to π‘Œ
  • D 𝑅 = { ( 1 4 , 4 2 ) , ( 7 , 2 1 ) } , a function from 𝑋 to π‘Œ , range = { 4 2 , 2 1 }
Preview