Worksheet: Representing Relations

In this worksheet, we will practice representing a relation using a mapping diagram or a graph, knowing that a relation is a set of inputs and outputs.

Q1:

Write the relation 𝑅 for the following arrow diagram:

  • A 𝑅 = { ( 6 , 8 ) , ( 1 0 , 1 2 ) , ( 1 1 , 1 3 ) , ( 8 , 6 ) , ( 1 2 , 1 0 ) , ( 1 3 , 1 1 ) }
  • B 𝑅 = { ( 8 , 6 ) , ( 1 2 , 1 0 ) , ( 1 3 , 1 1 ) }
  • C 𝑅 = { ( 6 , 8 ) , ( 1 0 , 1 3 ) , ( 1 1 , 1 2 ) }
  • D 𝑅 = { ( 6 , 8 ) , ( 1 0 , 1 2 ) , ( 1 1 , 1 3 ) }
  • E 𝑅 = { ( 6 , 8 ) , ( 1 0 , 1 2 ) , ( 1 3 , 1 1 ) }

Q2:

In basketball, each shot made from outside the 3-point line scores 3 points. The table shows this relationship. List this information as coordinates (3-point shots made, total number of points).

3-Point Shots Made 0 1 2 3
Total Points 0 3 6 9
  • A , , ,
  • B , , ,
  • C , , ,
  • D , , ,
  • E , , ,

Q3:

Using the Cartesian diagram below, determine the relation 𝑅 , where 𝑅 𝑥 𝑦 .

  • A 𝑅 = { ( 2 , 4 ) , ( 4 , 6 ) , ( 8 , 1 0 ) , ( 4 , 2 ) , ( 6 , 4 ) , ( 1 0 , 8 ) , }
  • B 𝑅 = { ( 4 , 2 ) , ( 6 , 4 ) , ( 1 0 , 8 ) , }
  • C 𝑅 = { ( 2 , 4 ) , ( 4 , 1 0 ) , ( 8 , 6 ) , }
  • D 𝑅 = { ( 2 , 4 ) , ( 4 , 6 ) , ( 8 , 1 0 ) , }
  • E 𝑅 = { ( 2 , 4 ) , ( 4 , 6 ) , ( 1 0 , 8 ) , }

Q4:

Write the relation 𝑅 for the following arrow diagram:

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

Q5:

Given that 𝑎 𝑥 and 𝑏 𝑦 , express the following arrow diagram in the form of an equation.

  • A 𝑎 + 𝑏 = 2
  • B 𝑏 = 𝑎 + 2
  • C 5 𝑎 = 3 𝑏
  • D 𝑏 = 𝑎 2
  • E 𝑏 = 3 5 𝑎

Q6:

Given that 𝑅 is a relation from 𝑋 to 𝑌 , where 𝑎 𝑋 and 𝑏 𝑌 , which of the following equations correctly expresses relation 𝑅 ?

  • A 𝑎 = 2 𝑏 2
  • B 𝑏 = 2 𝑎 2
  • C 𝑎 = 2 𝑏 + 2
  • D 𝑏 = 2 𝑎 + 2
  • E 𝑏 = 𝑎 + 1

Q7:

Which of the following correctly express the relation 𝑅 illustrated in the figure below?

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

Q8:

Which of the following relations correctly express the mapping diagram shown in the figure below?

  • A 𝑅 = { ( 4 , 4 ) , ( 7 , 7 ) , ( 4 , 6 ) , ( 5 , 8 ) , ( 6 , 5 ) , ( 7 , 8 ) }
  • B 𝑅 = { ( 4 , 4 ) , ( 8 , 8 ) , ( 4 , 6 ) , ( 5 , 8 ) , ( 6 , 5 ) , ( 7 , 8 ) }
  • C 𝑅 = { ( 4 , 4 ) , ( 7 , 7 ) , ( 8 , 8 ) , ( 6 , 4 ) , ( 8 , 5 ) , ( 5 , 6 ) , ( 8 , 7 ) }
  • D 𝑅 = { ( 4 , 4 ) , ( 7 , 7 ) , ( 8 , 8 ) , ( 4 , 6 ) , ( 5 , 8 ) , ( 6 , 5 ) , ( 7 , 8 ) }
  • E 𝑅 = { ( 4 , 4 ) , ( 7 , 7 ) , ( 8 , 8 ) , ( 8 , 5 ) , ( 5 , 6 ) , ( 8 , 7 ) }

Q9:

Write the relation 𝑅 for the following arrow diagram:

  • A 𝑅 = { ( 6 , 1 1 ) , ( 9 , 1 4 ) , ( 1 0 , 1 5 ) , ( 1 1 , 6 ) , ( 1 4 , 9 ) , ( 1 5 , 1 0 ) }
  • B 𝑅 = { ( 1 1 , 6 ) , ( 1 4 , 9 ) , ( 1 5 , 1 0 ) }
  • C 𝑅 = { ( 6 , 1 1 ) , ( 9 , 1 5 ) , ( 1 0 , 1 4 ) }
  • D 𝑅 = { ( 6 , 1 1 ) , ( 9 , 1 4 ) , ( 1 0 , 1 5 ) }
  • E 𝑅 = { ( 6 , 1 1 ) , ( 9 , 1 4 ) , ( 1 5 , 1 0 ) }

Q10:

Write the relation 𝑅 for the following arrow diagram:

  • A 𝑅 = { ( 5 , 1 ) , ( 2 , 4 ) , ( 0 , 6 ) , ( 1 , 5 ) , ( 4 , 2 ) , ( 6 , 0 ) }
  • B 𝑅 = { ( 1 , 5 ) , ( 4 , 2 ) , ( 6 , 0 ) }
  • C 𝑅 = { ( 5 , 1 ) , ( 2 , 6 ) , ( 0 , 4 ) }
  • D 𝑅 = { ( 5 , 1 ) , ( 2 , 4 ) , ( 0 , 6 ) }
  • E 𝑅 = { ( 5 , 1 ) , ( 2 , 4 ) , ( 6 , 0 ) }

Q11:

Write the relation 𝑅 for the following arrow diagram:

  • A 𝑅 = { ( 8 , 3 ) , ( 7 , 2 ) , ( 6 , 1 ) , ( 3 , 8 ) , ( 2 , 7 ) , ( 1 , 6 ) }
  • B 𝑅 = { ( 3 , 8 ) , ( 2 , 7 ) , ( 1 , 6 ) }
  • C 𝑅 = { ( 8 , 3 ) , ( 7 , 1 ) , ( 6 , 2 ) }
  • D 𝑅 = { ( 8 , 3 ) , ( 7 , 2 ) , ( 6 , 1 ) }
  • E 𝑅 = { ( 8 , 3 ) , ( 7 , 2 ) , ( 1 , 6 ) }

Q12:

Write the relation 𝑅 for the following arrow diagram:

  • A 𝑅 = { ( 1 , 2 ) , ( 2 , 5 ) , ( 5 , 8 ) , ( 2 , 1 ) , ( 5 , 2 ) , ( 8 , 5 ) }
  • B 𝑅 = { ( 2 , 1 ) , ( 5 , 2 ) , ( 8 , 5 ) }
  • C 𝑅 = { ( 1 , 2 ) , ( 2 , 8 ) , ( 5 , 5 ) }
  • D 𝑅 = { ( 1 , 2 ) , ( 2 , 5 ) , ( 5 , 8 ) }
  • E 𝑅 = { ( 1 , 2 ) , ( 2 , 5 ) , ( 8 , 5 ) }

Q13:

Using the Cartesian diagram below, determine the relation 𝑅 , where 𝑅 𝑥 𝑦 .

  • A 𝑅 = { ( 5 , 1 0 ) , ( 1 0 , 1 5 ) , ( 2 0 , 2 5 ) , ( 1 0 , 5 ) , ( 1 5 , 1 0 ) , ( 2 5 , 2 0 ) , }
  • B 𝑅 = { ( 1 0 , 5 ) , ( 1 5 , 1 0 ) , ( 2 5 , 2 0 ) , }
  • C 𝑅 = { ( 5 , 1 0 ) , ( 1 0 , 2 5 ) , ( 2 0 , 1 5 ) , }
  • D 𝑅 = { ( 5 , 1 0 ) , ( 1 0 , 1 5 ) , ( 2 0 , 2 5 ) , }
  • E 𝑅 = { ( 5 , 1 0 ) , ( 1 0 , 1 5 ) , ( 2 5 , 2 0 ) , }

Q14:

Using the Cartesian diagram below, determine the relation 𝑅 , where 𝑅 𝑥 𝑦 .

  • A 𝑅 = { ( 4 , 8 ) , ( 8 , 1 2 ) , ( 1 6 , 2 0 ) , ( 8 , 4 ) , ( 1 2 , 8 ) , ( 2 0 , 1 6 ) , }
  • B 𝑅 = { ( 8 , 4 ) , ( 1 2 , 8 ) , ( 2 0 , 1 6 ) , }
  • C 𝑅 = { ( 4 , 8 ) , ( 8 , 2 0 ) , ( 1 6 , 1 2 ) , }
  • D 𝑅 = { ( 4 , 8 ) , ( 8 , 1 2 ) , ( 1 6 , 2 0 ) , }
  • E 𝑅 = { ( 4 , 8 ) , ( 8 , 1 2 ) , ( 2 0 , 1 6 ) , }

Q15:

Using the Cartesian diagram below, determine the relation 𝑅 , where 𝑅 𝑥 𝑦 .

  • A 𝑅 = { ( 3 , 6 ) , ( 6 , 9 ) , ( 1 2 , 1 5 ) , ( 6 , 3 ) , ( 9 , 6 ) , ( 1 5 , 1 2 ) , }
  • B 𝑅 = { ( 6 , 3 ) , ( 9 , 6 ) , ( 1 5 , 1 2 ) , }
  • C 𝑅 = { ( 3 , 6 ) , ( 6 , 1 5 ) , ( 1 2 , 9 ) , }
  • D 𝑅 = { ( 3 , 6 ) , ( 6 , 9 ) , ( 1 2 , 1 5 ) , }
  • E 𝑅 = { ( 3 , 6 ) , ( 6 , 9 ) , ( 1 5 , 1 2 ) , }

Q16:

Using the Cartesian diagram below, determine the relation 𝑅 , where 𝑅 𝑥 𝑦 .

  • A 𝑅 = { ( 6 , 1 2 ) , ( 1 2 , 1 8 ) , ( 2 4 , 3 0 ) , ( 1 2 , 6 ) , ( 1 8 , 1 2 ) , ( 3 0 , 2 4 ) , }
  • B 𝑅 = { ( 1 2 , 6 ) , ( 1 8 , 1 2 ) , ( 3 0 , 2 4 ) , }
  • C 𝑅 = { ( 6 , 1 2 ) , ( 1 2 , 3 0 ) , ( 2 4 , 1 8 ) , }
  • D 𝑅 = { ( 6 , 1 2 ) , ( 1 2 , 1 8 ) , ( 2 4 , 3 0 ) , }
  • E 𝑅 = { ( 6 , 1 2 ) , ( 1 2 , 1 8 ) , ( 3 0 , 2 4 ) , }

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