Worksheet: Determining Whether a Relation Is a Function

In this worksheet, we will practice determining whether a given relation is a function.

Q1:

Which of the following relations represents a function?

Relation A ( 4 , 1 2 ) ( 4 , 1 5 ) ( 5 , 1 8 ) ( 5 , 2 1 ) ( 6 , 2 4 )
Relation B ( 4 , 1 2 ) ( 5 , 1 5 ) ( 6 , 1 8 ) ( 7 , 2 1 ) ( 8 , 2 4 )
  • ARelation B
  • BRelation A

Q2:

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

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

Q3:

Which of the following represents a function with input 𝑋 and output 𝑌 ?

Relation A
𝑋 3 0 3 8 1 0
𝑌 6 8 20 4 8
Relation B
𝑋 2 0 2 7 8
𝑌 6 8 20 4 8
  • ARelation A
  • BRelation B

Q4:

Which of the following relations represents a function?

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

Q5:

If a graph represents a function, how many points of intersection does it have with a vertical line?

  • Aone point
  • Btwo or more points

Q6:

If 𝑋 = { 4 , 3 , 2 , 1 , 0 } , 𝑌 = 1 1 6 , 1 8 , 1 4 , 1 2 , 1 , 2 , 4 , 8 , and 𝑅 is the relation from 𝑋 to 𝑌 , where 𝑎 𝑅 𝑏 means 𝑏 = 2 , determine whether 𝑅 represents a function or not.

  • Ayes
  • Bno

Q7:

Which of the following assigns only one 𝑦 -value to each 𝑥 -value?

  • A 𝑥 = 𝑦 2
  • B 𝑦 = 3 𝑥 + 6 2
  • C 𝑦 = ± 𝑥
  • D 𝑦 = 8 𝑥
  • E 𝑦 = 3 𝑥 6 2

Q8:

Suppose 𝑋 = { 𝑎 , 𝑏 , 𝑐 } and 𝑌 = { 1 , 2 } . How many different functions are there from 𝑋 to 𝑌 ?

Q9:

Suppose 𝐴 = { 𝑎 } and 𝐵 = { 1 , 2 } . How many different functions are there from 𝐴 to 𝐵 ?

Q10:

If 𝑋 = { 𝑥 𝑥 , 1 𝑥 4 } , and 𝑎 𝑅 𝑏 means that 𝑎 + 𝑏 is divisible by 5, where 𝑅 is a relation on 𝑋 , determine whether 𝑅 represents a function where 𝑎 𝑋 and 𝑏 𝑋 .

  • AIt does.
  • BIt does not.

Q11:

Given that 𝑥 and 𝑦 are real variables, which of the following relations is a function of 𝑥 ?

  • A 𝑦 = 8 𝑥 4
  • B 𝑦 = 8 𝑥 4 𝑥 t a n c o s
  • C 𝑦 + 𝑥 = 6 4
  • D 𝑦 = 8 𝑥 4 𝑥 t a n c o s
  • E 8 𝑦 = 4 𝑦 8 𝑥

Q12:

Suppose 𝐴 = { 𝑎 } and 𝐵 is a set with 𝑛 elements. How many different functions are there from 𝐴 to 𝐵 ?

  • A It is not possible to say.
  • B 1
  • C
  • D 𝑛
  • E 𝑛 + 1

Q13:

𝑋 = { 2 , 4 , 8 } , 𝑌 = { 8 , 1 3 , 1 5 , 1 9 } , and 𝑅 is a relation from 𝑋 to 𝑌 . If 𝑎 𝑋 and 𝑏 𝑌 , which of the following relations represents a function?

  • A 𝑎 is twice 𝑏
  • B 𝑎 + 𝑏 < 8
  • C 𝑏 is twice 𝑎
  • D 𝑎 is a factor of 𝑏
  • E 𝑎 2 𝑏 = an odd number

Q14:

Suppose 𝐴 = { 𝑥 , 𝑥 } 1 2 and 𝐵 = { 1 , 2 } . How many different functions are there from 𝐴 to 𝐵 ?

Q15:

Given that 𝑋 = { 𝑎 , 𝑏 , 𝑐 } , 𝑌 = { 7 , 2 0 , 1 , 1 7 , 1 4 } , and 𝑅 = { ( 𝑎 , 1 4 ) , ( 𝑏 , 7 ) , ( 𝑐 , 1 7 ) } , where 𝑅 is a relation from 𝑋 to 𝑌 , does 𝑅 represent a function?

  • Ayes
  • Bno

Q16:

If 𝑋 = { 5 , 4 , 8 } , 𝑌 = { 4 9 , 1 6 , 6 4 } , and 𝑅 is a relation from 𝑋 to 𝑌 , where 𝑎 𝑅 𝑏 means 𝑎 = 𝑏 ; 𝑎 𝑋 and 𝑏 𝑌 , does 𝑅 represent a function?

  • Ano
  • Byes

Q17:

Given that 𝑋 = { 7 , 7 , 3 } , 𝑌 = { 5 8 , 1 3 , 𝑙 } , and 𝑎 𝑅 𝑏 is represented by the equation 𝑏 = 𝑎 + 9 , where 𝑅 is a function from 𝑋 to 𝑌 , for which 𝑎 𝑋 and 𝑏 𝑌 , determine the value of 𝑙 .

Q18:

Suppose 𝐴 = { 𝑥 , 𝑥 } 1 2 and 𝐵 = { 1 } . How many different functions are there from 𝐴 to 𝐵 ?

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