Worksheet: Domain and Range of a Piecewise Function

In this worksheet, we will practice finding the domain and range of a piecewise-defined function.

Q1:

Find the range of the function

  • A 0 , 4
  • B [ 5 , 3 ]
  • C ] , 4 ]
  • D [ 0 , 4 ]

Q2:

Determine the domain of the function

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

Q3:

Determine the domain and the range of the function 𝑓 ( 𝑥 ) = 6 𝑥 < 0 , 4 𝑥 > 0 . i f i f

  • A The domain is { 4 , 6 } , and the range is { 0 } .
  • B The domain is , and the range is { 4 , 6 } .
  • C The domain is { 4 , 6 } , and the range is .
  • D The domain is { 0 } , and the range is { 4 , 6 } .
  • E The domain is { 6 , 4 } , and the range is { 4 , 6 } .

Q4:

Find the domain of the real function

  • A ] 1 5 , 5 0 ]
  • B [ 1 5 , 5 0 [
  • C [ 1 5 , 5 0 ]
  • D ] 1 5 , 5 0 [

Q5:

Determine the intervals of increase and decrease of the function

  • A 𝑓 ( 𝑥 ) is increasing everywhere.
  • B 𝑓 ( 𝑥 ) is increasing on the interval ] , 0 [ and decreasing on the interval ] 0 , [ .
  • C 𝑓 ( 𝑥 ) is decreasing everywhere.
  • D 𝑓 ( 𝑥 ) is increasing on the interval ] 0 , [ and decreasing on the interval ] , 0 [ .
  • E 𝑓 ( 𝑥 ) is increasing on the interval ] 8 , [ and decreasing on the interval ] , 8 [ .

Q6:

Find the domain and the range of the function

  • A domain = + , range =
  • B domain = , range =
  • C domain = ] 1 , [ , range =
  • D domain = , range = ] 0 , [
  • E domain = , range = ] 4 , [

Q7:

Determine the range of the function

  • A
  • B
  • C
  • D
  • E

Q8:

Find the range of the function

  • A { 0 , 1 }
  • B [ 0 , 8 ]
  • C { 0 , 8 }
  • D [ 0 , 1 ]
  • E { 0 , 8 }

Q9:

Find the domain of the function

  • A { 0 , 1 }
  • B [ 0 , 1 ]
  • C { 0 , 8 }
  • D [ 0 , 8 ]
  • E { 0 , 8 }

Q10:

Find the domain of the real function

  • A ] 2 3 , [
  • B [ 2 3 , [
  • C ] , 2 3 ]
  • D ] , 2 3 [
  • E [ 6 , 2 3 [

Q11:

Determine the domain of the function

  • A { 8 , 1 }
  • B { 8 , 2 }
  • C [ 8 , 1 ]
  • D [ 8 , 2 ]
  • E { 8 , 1 }

Q12:

Determine the domain of the function

  • A { 1 , 0 }
  • B [ 1 , 0 ]
  • C { 0 , 5 }
  • D [ 0 , 5 ]
  • E { 0 , 5 }

Q13:

Find the domain of the real function

  • A ] 8 , 2 3 [
  • B [ 8 , 2 3 ]
  • C ] 8 , 2 3 ]
  • D [ 8 , 2 3 [

Q14:

Find the domain of the function

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

Q15:

Determine the domain of the function

  • A { 0 , 1 2 }
  • B [ 0 , 1 2 ]
  • C
  • D [ 4 , 9 ]
  • E { 4 , 9 }

Q16:

Determine the domain of the function

  • A { 0 , 8 }
  • B [ 0 , 8 ]
  • C
  • D [ 1 , 8 ]
  • E { 1 , 8 }

Q17:

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

  • A { 2 , 3 }
  • B { 2 , 6 }
  • C [ 2 , 3 ]
  • D [ 0 , 4 ]
  • E { 2 , 3 }

Q18:

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

  • A { 1 }
  • B
  • C { 4 }
  • D [ 1 , 7 ]
  • E [ 1 , )

Q19:

Find the range of the following function.

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

Q20:

Determine the range of the function

  • A { 0 , 5 }
  • B [ 6 , 1 ]
  • C
  • D [ 0 , 5 ]
  • E { 6 , 1 }

Q21:

Determine the range of the function

  • A { 7 , 3 }
  • B { 0 , 3 }
  • C { 7 , 6 }
  • D [ 7 , 3 ]

Q22:

Find the range of the function