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Lesson: Domain and Range of a Piecewise Function

In this lesson, we will learn how to find the domain and range of a piecewise-defined function.

Sample Question Videos

01:46
01:38

Worksheet • 25 Questions • 2 Videos

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

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

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

Q6:

Find the domain and the range of the function

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

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 ℝ − { 0 , 8 }
  • E ℝ − { 0 , 1 }

Q9:

Find the domain of the function

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

Q10:

Find the domain of the real function

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

Q11:

Determine the domain of the function

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

Q12:

Determine the domain of the function

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

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

Q15:

Determine the domain of the function

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

Q16:

Determine the domain of the function

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

Q17:

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

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

Q18:

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

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

Q19:

Find the range of the following function.

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

Q20:

Determine the range of the function

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

Q21:

Determine the range of the function