Lesson Worksheet: Relations and Functions Mathematics • 8th Grade

In this worksheet, we will practice identifying, representing, and recognizing functions from schematic descriptions, arrow diagrams, and graphs.

Q1:

Which of the following relations represents a function?

Relation A(4,12)(4,15)(5,18)(5,21)(6,24)
Relation B(4,12)(5,15)(6,18)(7,21)(8,24)
  • ARelation A
  • BRelation B

Q2:

Which of the following is the best description for a function?

  • AA function is a relation that assigns to each input exactly one output.
  • BA function is a mathematical rule that assigns to each input more than one output.
  • CA function is a relation such that every input is mapped to multiple outputs.

Q3:

Which of the following represents a function with input 𝑋 and output π‘Œ?

Relation A
π‘‹βˆ’3038βˆ’10
π‘Œ682048
Relation B
π‘‹βˆ’20βˆ’27βˆ’8
π‘Œ682048
  • ARelation B
  • BRelation A

Q4:

Which of the following relations represents a function?

  • A(c)
  • B(b)
  • C(a) and (c)
  • D(a)
  • Eall

Q5:

If 𝑋={βˆ’4,βˆ’3,βˆ’2,βˆ’1,0}, π‘Œ=116,18,14,12,1,2,4,8, and 𝑅 is the relation from 𝑋 to π‘Œ, where π‘Žπ‘…π‘ means 𝑏=2, determine whether 𝑅 represents a function or not.

  • AYes
  • BNo

Q6:

Which of the following assigns only one 𝑦-value to each π‘₯-value?

  • A𝑦=βˆ’3π‘₯βˆ’6
  • B𝑦=8π‘₯
  • Cπ‘₯=π‘¦οŠ¨
  • D𝑦=±√π‘₯
  • E𝑦=βˆ’3π‘₯+6

Q7:

Suppose 𝑋={π‘Ž,𝑏,𝑐} and π‘Œ={1,2}. How many different functions are there from 𝑋 to π‘Œ?

Q8:

Suppose 𝐴={π‘Ž} and 𝐡={1,2}. How many different functions are there from 𝐴 to 𝐡?

Q9:

If 𝑋={π‘₯∢π‘₯βˆˆβ„•,1≀π‘₯≀4}, and π‘Žπ‘…π‘ means that π‘Ž+𝑏 is divisible by 5, where 𝑅 is a relation on 𝑋, determine whether 𝑅 represents a function where π‘Žβˆˆπ‘‹ and π‘βˆˆπ‘‹.

  • AIt does not.
  • BIt does.

Q10:

Suppose 𝐴={π‘Ž} and 𝐡 is a set with 𝑛 elements. How many different functions are there from 𝐴 to 𝐡?

  • A𝑛+1
  • B𝑛
  • C∞
  • DIt is not possible to say.
  • E1

Q11:

𝑋={2,4,8}, π‘Œ={8,13,15,19}, and 𝑅 is a relation from 𝑋 to π‘Œ. If π‘Žβˆˆπ‘‹ and π‘βˆˆπ‘Œ, which of the following relations represents a function?

  • Aπ‘Ž is a factor of 𝑏
  • Bπ‘Ž+𝑏<8
  • Cπ‘Žβˆ’2𝑏= an odd number
  • Dπ‘Ž is twice 𝑏
  • E𝑏 is twice π‘Ž

Q12:

Suppose 𝐴={π‘₯,π‘₯} and 𝐡={1,2}. How many different functions are there from 𝐴 to 𝐡?

Q13:

Given that 𝑋={π‘Ž,𝑏,𝑐}, π‘Œ={7,20,1,17,14}, and 𝑅={(π‘Ž,14),(𝑏,7),(𝑐,17)}, where 𝑅 is a relation from 𝑋 to π‘Œ, does 𝑅 represent a function?

  • ANo
  • BYes

Q14:

If 𝑋={5,4,8}, π‘Œ={49,16,64}, and 𝑅 is a relation from 𝑋 to π‘Œ, where π‘Žπ‘…π‘ means π‘Ž=βˆšπ‘; π‘Žβˆˆπ‘‹ and π‘βˆˆπ‘Œ, does 𝑅 represent a function?

  • AYes
  • BNo

Q15:

Given that 𝑋={βˆ’7,7,3}, π‘Œ={58,13,𝑙}, and π‘Žπ‘…π‘ is represented by the equation 𝑏=π‘Ž+9, where 𝑅 is a function from 𝑋 to π‘Œ, for which π‘Žβˆˆπ‘‹ and π‘βˆˆπ‘Œ, determine the value of 𝑙.

Q16:

Suppose 𝐴={π‘₯,π‘₯} and 𝐡={1}. How many different functions are there from 𝐴 to 𝐡?

Q17:

Let 𝑓={(π‘Ž,1),(𝑏,3),(𝑐,βˆ’1)(𝑑,3)}. Is 𝑓 a function?

  • ANo
  • BYes

Q18:

Given that 𝑋={16,8,20}, π‘Œ={13,7}, and 𝑅={(16,13),(8,13),(π‘Ž,13)}, where 𝑅 is a function from 𝑋 to π‘Œ, find the numerical value of π‘Ž.

Q19:

Which of the following relations represents a function from 𝑋 to π‘Œ?

  • A(𝑅2)
  • B(𝑅1)
  • C(𝑅4)
  • D(𝑅3)

Q20:

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

  • ATrue
  • BFalse

Q21:

Which of the following relations represents a function?

  • ARelation B
  • BRelation A

Q22:

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

  • ANo
  • BYes

Q23:

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?

  • A𝑓={9,2,4,7}
  • B𝑓={(2,9),(4,2),(7,4),(9,7)}
  • C𝑓={(2,7),(4,2),(7,9),(9,4)}
  • D𝑓={(2,4),(4,7),(7,9),(9,2)}
  • E𝑓={(2,2),(4,4),(7,7),(9,9)}

Q24:

In a discussion between Madison and Benjamin about functions, Benjamin said that the diagram below represents a function but Madison argued that it does not. Who is right?

  • AMadison
  • BBenjamin

Q25:

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

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

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