Worksheet: Recognizing Functions from Diagrams and Sets

In this worksheet, we will practice identifying and representing a function.

Q1:

Does the relation shown by the arrow diagram represent a function?

  • Ano
  • Byes

Q2:

Which of the relations shown by the set of the ordered pairs below does not represent a function?

  • A { ( 3 , 1 1 ) , ( 4 , 1 1 ) , ( 5 , 1 1 ) , ( 6 , 1 1 ) }
  • B { ( 3 , 1 1 ) , ( 1 1 , 1 9 ) , ( 2 7 , 3 5 ) , ( 4 3 , 4 3 ) }
  • C { ( 8 , 4 ) , ( 9 , 4 ) , ( 1 0 , 4 ) , ( 1 1 , 4 ) }
  • D { ( 3 , 4 ) , ( 1 1 , 8 ) , ( 3 , 1 2 ) , ( 1 1 , 1 1 ) }

Q3:

If 𝑓 is a function on 𝑋 , where 𝑋 = { 2 , 4 , 7 , 9 } , 𝑓 ( 2 ) = 9 , 𝑓 ( 4 ) = 2 , 𝑓 ( 7 ) = 4 , and 𝑓 ( 9 ) = 7 , which of the following statements is true?

  • A 𝑓 = { 9 , 2 , 4 , 7 }
  • B 𝑓 = { ( 2 , 4 ) , ( 4 , 7 ) , ( 7 , 9 ) , ( 9 , 2 ) }
  • C 𝑓 = { ( 2 , 2 ) , ( 4 , 4 ) , ( 7 , 7 ) , ( 9 , 9 ) }
  • D 𝑓 = { ( 2 , 9 ) , ( 4 , 2 ) , ( 7 , 4 ) , ( 9 , 7 ) }
  • E 𝑓 = { ( 2 , 7 ) , ( 4 , 2 ) , ( 7 , 9 ) , ( 9 , 4 ) }

Q4:

Which of the following relations represents a function from 𝑋 to 𝑌 ?

  • A ( 𝑅 3 )
  • B ( 𝑅 2 )
  • C ( 𝑅 4 )
  • D ( 𝑅 1 )

Q5:

Which of the following relations represents a function?

  • ARelation A
  • BRelation B

Q6:

Determine whether the following statement is true or false: The given figure represents a function.

  • Afalse
  • Btrue

Q7:

Given that 𝑋 = { 2 , 3 , 4 } , which of the following relations defines a function on the domain 𝑋 ?

  • A { ( 2 , 2 ) , ( 3 , 3 ) , ( 3 , 4 ) }
  • B { ( 2 , 2 ) , ( 2 , 3 ) , ( 2 , 4 ) }
  • C { ( 2 , 2 ) , ( 3 , 3 ) }
  • D { ( 2 , 2 ) , ( 3 , 2 ) , ( 4 , 2 ) }
  • E { ( 3 , 3 ) , ( 4 , 4 ) }

Q8:

Which of the following Cartesian diagrams represents a function from 𝑥 to 𝑥 ?

  • A(c)
  • B(b)
  • C(d)
  • D(a)

Q9:

Which of the following relations represents a function given that 𝑥 is the input and 𝑦 is the output.

  • A(b)
  • B(a)

Q10:

If 𝑓 is a function on 𝑋 , where 𝑋 = { 5 , 7 , 9 , 1 0 } , 𝑓 ( 5 ) = 7 , 𝑓 ( 7 ) = 5 , 𝑓 ( 9 ) = 9 , and 𝑓 ( 1 0 ) = 1 0 , which of the following statements is true?

  • A 𝑓 = { ( 5 , 5 ) , ( 7 , 7 ) , ( 9 , 9 ) , ( 1 0 , 1 0 ) }
  • B 𝑓 = { 7 , 5 , 9 , 1 0 }
  • C 𝑓 = { ( 5 , 9 ) , ( 7 , 5 ) , ( 9 , 1 0 ) , ( 1 0 , 7 ) }
  • D 𝑓 = { ( 5 , 7 ) , ( 7 , 5 ) , ( 9 , 9 ) , ( 1 0 , 1 0 ) }

Q11:

If 𝑓 is a function on 𝑋 , where 𝑋 = { 7 , 6 , 4 , 2 } , 𝑓 ( 7 ) = 6 , 𝑓 ( 6 ) = 4 , 𝑓 ( 4 ) = 7 , and 𝑓 ( 2 ) = 2 , which of the following statements is true?

  • A 𝑓 = { 6 , 4 , 7 , 2 }
  • B 𝑓 = { ( 7 , 4 ) , ( 6 , 7 ) , ( 4 , 6 ) , ( 2 , 2 ) }
  • C 𝑓 = { ( 7 , 7 ) , ( 6 , 6 ) , ( 4 , 4 ) , ( 2 , 2 ) }
  • D 𝑓 = { ( 7 , 6 ) , ( 6 , 4 ) , ( 4 , 7 ) , ( 2 , 2 ) }
  • E 𝑓 = { ( 7 , 4 ) , ( 6 , 7 ) , ( 4 , 2 ) , ( 2 , 6 ) }

Q12:

Does the relation shown by the arrow diagram represent a function?

  • Ayes
  • Bno

Q13:

Does the relation shown by the arrow diagram represent a function?

  • Ayes
  • Bno

Q14:

Does the relation shown by the arrow diagram represent a function?

  • Ayes
  • Bno

Q15:

Which of the following relations represents a function from 𝑋 to 𝑌 ?

  • A ( 𝑅 3 )
  • B ( 𝑅 1 )
  • C ( 𝑅 4 )
  • D ( 𝑅 2 )

Q16:

Given that 𝑋 = { 8 , 9 , 1 0 } , which of the following relations defines a function on the domain 𝑋 ?

  • A { ( 8 , 8 ) , ( 9 , 9 ) , ( 9 , 1 0 ) }
  • B { ( 8 , 8 ) , ( 8 , 9 ) , ( 8 , 1 0 ) }
  • C { ( 8 , 8 ) , ( 9 , 9 ) }
  • D { ( 8 , 8 ) , ( 9 , 8 ) , ( 1 0 , 8 ) }
  • E { ( 9 , 9 ) , ( 1 0 , 1 0 ) }

Q17:

Given that 𝑋 = { 4 , 5 , 6 } , which of the following relations defines a function on the domain 𝑋 ?

  • A { ( 4 , 4 ) , ( 5 , 5 ) , ( 5 , 6 ) }
  • B { ( 4 , 4 ) , ( 4 , 5 ) , ( 4 , 6 ) }
  • C { ( 4 , 4 ) , ( 5 , 5 ) }
  • D { ( 4 , 4 ) , ( 5 , 4 ) , ( 6 , 4 ) }
  • E { ( 5 , 5 ) , ( 6 , 6 ) }

Q18:

Given that 𝑋 = { 1 3 , 1 4 , 1 5 } , which of the following relations defines a function on the domain 𝑋 ?

  • A { ( 1 3 , 1 3 ) , ( 1 4 , 1 4 ) , ( 1 4 , 1 5 ) }
  • B { ( 1 3 , 1 3 ) , ( 1 3 , 1 4 ) , ( 1 3 , 1 5 ) }
  • C { ( 1 3 , 1 3 ) , ( 1 4 , 1 4 ) }
  • D { ( 1 3 , 1 3 ) , ( 1 4 , 1 3 ) , ( 1 5 , 1 3 ) }
  • E { ( 1 4 , 1 4 ) , ( 1 5 , 1 5 ) }

Q19:

Given that 𝑋 = { 1 , 2 , 3 } , which of the following relations defines a function on the domain 𝑋 ?

  • A { ( 1 , 1 ) , ( 2 , 2 ) , ( 2 , 3 ) }
  • B { ( 1 , 1 ) , ( 1 , 2 ) , ( 1 , 3 ) }
  • C { ( 1 , 1 ) , ( 2 , 2 ) }
  • D { ( 1 , 1 ) , ( 2 , 1 ) , ( 3 , 1 ) }
  • E { ( 2 , 2 ) , ( 3 , 3 ) }

Q20:

Which of the following Cartesian diagrams represents a function from 𝑥 to 𝑥 ?

  • A(c)
  • B(a)
  • C(d)
  • D(b)

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