Worksheet: Domain and Range of the Absolute Value Function

In this worksheet, we will practice finding the domain and range of absolute value functions.

Q1:

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

  • A The domain is { 1 } and the range is ] 1 , [ .
  • B The domain is [ 1 , [ and the range is .
  • C The domain is ] 1 , [ and the range is { 1 } .
  • D The domain is and the range is [ 1 , [ .

Q2:

Find the range of the function 𝑓 ( 𝑥 ) = | 2 𝑥 2 | .

  • A { 1 }
  • B
  • C [ 1 , [
  • D [ 0 , [
  • E { 1 }

Q3:

Find the range of the function 𝑓 ( 𝑥 ) = | 2 𝑥 + 1 | .

  • A 1 2
  • B
  • C 1 2 ,
  • D [ 0 , [

Q4:

Find the domain of the function 𝑓 ( 𝑥 ) = | 3 𝑥 8 | .

  • A 8 3
  • B [ 0 , )
  • C 8 3 ,
  • D

Q5:

Find the domain and range of the function 𝑓 ( 𝑥 ) = | 3 𝑥 1 | + 3 𝑥 + 5 .

  • A The domain is 1 3 , , and the range is .
  • B The domain is , and the range is 1 3 , .
  • C The domain is 1 3 , , and the range is [ 6 , ) .
  • D The domain is , and the range is [ 6 , ) .

Q6:

Determine the domain and the range of the function 𝑓 ( 𝑥 ) = | 5 𝑥 + 5 | 9 .

  • A The domain is { 1 } , and the range is ] 9 , [ .
  • B The domain is [ 9 , [ , and the range is .
  • C The domain is ] 9 , [ , and the range is { 1 } .
  • D The domain is , and the range is [ 9 , [ .
  • E The domain is , and the range is [ 0 , [ .

Q7:

Given that 𝑎 is a constant, what is the domain of the function 𝑓 ( 𝑥 ) = | 𝑥 + 𝑎 | ?

  • A [ 𝑎 , [
  • B 𝑎
  • C ] , 𝑎 ]
  • D

Q8:

Find the domain and range of the function 𝑓 ( 𝑥 ) = 4 | 𝑥 5 | 1 .

  • A The domain is { 5 } and the range is { 1 } .
  • B The domain is ] , 1 ] and the range is .
  • C The domain is and the range is ] , 1 [ .
  • D The domain is and the range is ] , 1 ] .

Q9:

Given that 𝑎 is a constant, what is the domain of the function 𝑓 ( 𝑥 ) = | 𝑥 𝑎 | ?

  • A [ 𝑎 , [
  • B 𝑎
  • C ] , 𝑎 ]
  • D

Q10:

Find the domain of the function 𝑓 ( 𝑥 ) = | 8 𝑥 + 7 | .

  • A 7 8
  • B [ 0 , [
  • C 7 8 ,
  • D
  • E 7 8

Q11:

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

  • A The domain is { 1 } and the range is ] 1 , [ .
  • B The domain is [ 1 , [ and the range is .
  • C The domain is ] 1 , [ and the range is { 1 } .
  • D The domain is and the range is [ 1 , [ .

Q12:

Find the range of the function 𝑓 ( 𝑥 ) = | 𝑥 + 8 | .

  • A { 8 }
  • B
  • C [ 8 , [
  • D [ 0 , [

Q13:

Find the range of the function 𝑓 ( 𝑥 ) = | 𝑥 8 | .

  • A { 8 }
  • B
  • C [ 8 , [
  • D [ 0 , [

Q14:

Find the range of the function 𝑓 ( 𝑥 ) = | 2 𝑥 + 1 | .

  • A 1 2
  • B
  • C 1 2 ,
  • D [ 0 , [
  • E 1 2

Q15:

Find the range of the function 𝑓 ( 𝑥 ) = | 2 𝑥 + 2 | .

  • A { 1 }
  • B
  • C [ 1 , [
  • D [ 0 , [
  • E { 1 }

Q16:

Find the domain of the function 𝑓 ( 𝑥 ) = | 𝑥 + 4 | .

  • A { 4 }
  • B [ 0 , )
  • C [ 4 , )
  • D

Q17:

Find the domain of the function 𝑓 ( 𝑥 ) = | 𝑥 6 | .

  • A { 6 }
  • B [ 0 , )
  • C [ 6 , )
  • D

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