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

Q2:

Determine the domain of the function 𝑓 ( 𝑥 ) = 𝑥 𝑥 [ 0 , 1 ) , 1 𝑥 [ 1 , 8 ] , 9 𝑥 𝑥 ( 8 , 9 ] . i f i f i f

  • A [ 0 , 9 ]
  • B { 0 , 1 }
  • C { 0 , 9 }
  • D [ 0 , 1 ]
  • 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 , and the range is { 4 , 6 } .
  • B The domain is { 0 } , and the range is { 4 , 6 } .
  • C The domain is { 4 , 6 } , and the range is .
  • D The domain is { 6 , 4 } , and the range is { 4 , 6 } .
  • E The domain is { 4 , 6 } , and the range is { 0 } .

Q4:

Find the domain of the real function 𝑓 ( 𝑥 ) = 6 𝑥 1 5 < 𝑥 < 2 0 6 𝑥 2 0 𝑥 < 5 0 . i f i f

  • 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 𝑓 ( 𝑥 ) = 7 𝑥 8 𝑥 < 0 , 7 𝑥 8 𝑥 0 . i f i f

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

Q6:

Find the domain and the range of the function 𝑓 ( 𝑥 ) = 𝑥 + 1 𝑥 0 , 1 4 𝑥 > 0 . i f i f

  • A domain = , range = ( 0 , )
  • B domain = ( 1 , ) , range =
  • C domain = , range =
  • D domain = , range = ( 4 , )
  • E domain = , range =

Q7:

Determine the range of the function 𝑓 ( 𝑥 ) = 𝑥 + 2 𝑥 [ 2 , 3 ] , 5 𝑥 + 2 0 𝑥 ( 3 , 4 ] . i f i f

  • A { 0 , 5 }
  • B [ 2 , 4 ]
  • C
  • D [ 0 , 5 ]
  • E { 2 , 4 }

Q8:

Find the range of the function 𝑓 ( 𝑥 ) = 𝑥 𝑥 [ 0 , 1 ) , 1 𝑥 [ 1 , 7 ] , 8 𝑥 𝑥 ( 7 , 8 ] . i f i f i f

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

Q9:

Find the domain of the function 𝑓 ( 𝑥 ) = 𝑥 𝑥 [ 0 , 1 ) , 1 𝑥 [ 1 , 7 ] , 8 𝑥 𝑥 ( 7 , 8 ] . i f i f i f

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

Q10:

Find the domain of the real function 𝑓 ( 𝑥 ) = 𝑥 1 9 𝑥 6 , 1 9 6 < 𝑥 < 2 3 . i f i f

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

Q11:

Determine the domain of the function 𝑓 ( 𝑥 ) = 𝑥 8 𝑥 < 1 , 2 𝑥 1 𝑥 2 . i f i f

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

Q12:

Determine the domain of the function 𝑓 ( 𝑥 ) = 𝑥 𝑥 [ 0 , 1 ) , 1 𝑥 [ 1 , 2 ] , 5 𝑥 𝑥 ( 2 , 5 ] . i f i f i f

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

Q13:

Find the domain of the real function 𝑓 ( 𝑥 ) = 9 𝑥 𝑥 [ 8 , 1 2 ] , 1 0 8 𝑥 ( 1 2 , 1 8 ) , 𝑥 + 9 0 𝑥 [ 1 8 , 2 3 ) . i f i f i f

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

Q14:

Find the domain of the function 𝑓 ( 𝑥 ) = 𝑥 𝑥 [ 0 , 2 ) , 2 𝑥 [ 2 , 6 ] , 8 𝑥 𝑥 ( 6 , 8 ] . i f i f i f

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

Q15:

Determine the domain of the function 𝑓 ( 𝑥 ) = 𝑥 + 4 𝑥 [ 4 , 8 ] , 7 𝑥 6 3 𝑥 ( 8 , 9 ] . i f i f

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

Q16:

Determine the domain of the function 𝑓 ( 𝑥 ) = 𝑥 + 1 𝑥 [ 1 , 7 ] , 8 𝑥 + 6 4 𝑥 ( 7 , 8 ] . i f i f

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

Q17:

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

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

Q18:

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

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

Q19:

Find the range of the following function.

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

Q20:

Determine the range of the function 𝑓 ( 𝑥 ) = 𝑥 1 𝑥 [ 1 , 6 ] , 5 𝑥 + 3 5 𝑥 ( 6 , 7 ] . i f i f

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

Q21:

Determine the range of the function 𝑓 ( 𝑥 ) = 𝑥 7 𝑥 < 3 , 6 𝑥 3 𝑥 6 . i f i f

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

Q22:

Find the range of the function 𝑓 ( 𝑥 ) = 1 1 1 𝑥 1 1 , 𝑥 4 5 𝑥 1 9 . i f i f

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

Q23:

Find the range of the function 𝑓 ( 𝑥 ) = | 𝑥 + 9 | 8 𝑥 < 9 , ( 𝑥 + 9 ) 8 𝑥 9 . i f i f

  • A { 9 }
  • B { 8 }
  • C ( , 8 ]
  • D [ 8 , )

Q24:

Find the range of the function 𝑓 ( 𝑥 ) = 8 𝑥 𝑥 [ 0 , 1 ) , 8 𝑥 [ 1 , 7 ] , 1 5 𝑥 𝑥 ( 7 , 1 5 ] . i f i f i f

  • A [ 0 , 8 ]
  • B [ 0 , 9 ]
  • C { 0 , 8 }
  • D { 0 , 9 }
  • E { 0 , 9 }

Q25:

Determine the domain of the function represented by the following graph.

  • A ( 0 , ) { 3 }
  • B ( , 3 ] { 0 }
  • C ( 6 , )
  • D ( , 4 )

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