Worksheet: Intervals

In this worksheet, we will practice determining limited and unlimited intervals.

Q1:

The figure shows an interval on the number line. Write an expression for it using interval notation.

  • A [ 3 , 1 ]
  • B [ 3 , 1 )
  • C ( 3 , 1 )
  • D ( 3 , 1 ]

Q2:

Express the set of real numbers in the form of an interval.

  • A ( 0 , )
  • B ( , 0 )
  • C ( , 1 )
  • D ( 1 , )
  • E ( , )

Q3:

Which of the following is true?

  • A 1 6 ( 4 , )
  • B 1 6 ( 4 , )
  • C 1 6 ( 4 , )
  • D 1 6 ( 4 , )

Q4:

Which of the following is a half-open interval?

  • A { 1 , 9 }
  • B [ 1 , 9 ]
  • C ( 1 , 9 )
  • D [ 1 , 9 )

Q5:

Given that 𝑋=[8,3) and 𝑌=[4,3), find 𝑋𝑌.

  • A [ 4 , 3 )
  • B [ 8 , 4 ) [ 3 , 3 )
  • C [ 8 , 3 )
  • D

Q6:

Given that 𝑋=(3,4] and 𝑌=[6,2), find 𝑋𝑌.

  • A ( 3 , 4 ]
  • B [ 6 , 2 )
  • C [ 6 , 4 ]
  • D

Q7:

Which of the following expressions represents the set shown on the number line?

  • A [ 4 , 1 ]
  • B ( 4 , 1 )
  • C [ 4 , 1 )
  • D ( , 4 ] [ 1 , )
  • E ( 4 , 1 ]

Q8:

State the interval that is represented by the following number line.

  • A { 2 , 4 }
  • B ( 2 , 4 ]
  • C [ 2 , 4 ]
  • D [ 2 , 4 )
  • E ( 2 , 4 )

Q9:

Which of the following figures represents the interval (1,0]?

  • A(a)
  • B(b)
  • C(d)
  • D(c)

Q10:

Given that 𝑋=[7,2] and 𝑌=(2,), find 𝑌𝑋.

  • A ( 2 , )
  • B
  • C [ 7 , 2 ]
  • D [ 7 , )

Q11:

What is [5,4]?

  • A ( 0 , 4 ]
  • B [ 5 , 4 ]
  • C [ 5 , 0 ]
  • D [ 5 , 0 )

Q12:

Which of the following figures represents the set [2,4]?

  • A(c)
  • B(b)
  • C(d)
  • D(a)

Q13:

The figure shows an interval on the number line. Write an expression for the interval using set notation.

  • A 𝑋 = { 𝑥 6 < 𝑥 < 3 , 𝑥 }
  • B 𝑋 = { 𝑥 6 < 𝑥 3 , 𝑥 }
  • C 𝑋 = { 𝑥 6 𝑥 < 3 , 𝑥 }
  • D 𝑋 = { 𝑥 6 𝑥 3 , 𝑥 }

Q14:

Which of the following expressions represents the set shown on the number line?

  • A ( 4 , 1 ) { 3 }
  • B [ 4 , 3 ) { 1 }
  • C ( 4 , 3 ) { 1 }
  • D ( 4 , 3 ] { 1 }
  • E [ 4 , 3 ] { 1 }

Q15:

Express the following set using interval notation: 𝑋=𝑥𝑥8,𝑥.

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

Q16:

If 𝑥[1,625), what interval is 𝑥 in?

  • A [ 0 , 2 5 )
  • B [ 1 , 2 5 )
  • C [ 2 5 , 1 )
  • D [ 1 , 2 5 )
  • E [ 1 , 0 )

Q17:

Given that (,𝑘)[22,11]=[22,9), determine the value of 𝑘.

Q18:

Which of the following sets satisfies (17,15]𝑋=[20,15]?

  • A 𝑋 = ( 2 0 , 1 8 )
  • B 𝑋 = [ 1 7 , 1 6 ]
  • C 𝑋 = ( 1 7 , 1 6 )
  • D 𝑋 = [ 2 0 , 1 6 ]
  • E 𝑋 = [ 2 0 , 1 7 )

Q19:

Which of the following sets satisfies [15,0]𝑋=(15,0)?

  • A 𝑋 = ( 1 5 , 0 )
  • B 𝑋 = { 1 5 , 0 }
  • C 𝑋 = ( 1 5 , 0 ]
  • D 𝑋 =
  • E 𝑋 = [ 1 5 , 0 )

Q20:

Which of the following is true?

  • A 1 6 3 ( 9 , 5 )
  • B 1 6 3 ( 9 , 5 )
  • C 1 6 3 ( 9 , 5 )
  • D 1 6 3 ( 9 , 5 )

Q21:

Given that 𝑋=(6,6) and 𝑌={6,1}, find 𝑋𝑌.

  • A ( 6 , 6 )
  • B { 1 }
  • C [ 6 , 6 )
  • D { 6 , 1 }

Q22:

Which of the following is true?

  • A 1 [ 1 , )
  • B 1 [ 1 , )
  • C 1 [ 1 , )
  • D 1 [ 1 , )

Q23:

Which of the following is true?

  • A ( 2 , 7 ) ( , 9 ]
  • B ( 2 , 7 ) ( , 9 ]
  • C ( 2 , 7 ) ( , 9 ]
  • D ( 2 , 7 ) ( , 9 ]

Q24:

Given that 𝑋=[6,3] and 𝑌={4,3}, find 𝑋𝑌.

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

Q25:

Which of the following is true?

  • A | 1 2 | ( 1 1 , 1 5 )
  • B | 1 2 | ( 1 1 , 1 5 )
  • C | 1 2 | ( 1 1 , 1 5 )
  • D | 1 2 | ( 1 1 , 1 5 )

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