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Worksheet: Determining Whether a Relation Is a Function

Q1:

If 𝑋 = { βˆ’ 4 , βˆ’ 3 , βˆ’ 2 , βˆ’ 1 , 0 } , π‘Œ =  1 1 6 , 1 8 , 1 4 , 1 2 , 1 , 2 , 4 , 8  , and 𝑅 is the relation from 𝑋 to π‘Œ , where π‘Ž 𝑅 𝑏 means 𝑏 = 2 π‘Ž , determine whether 𝑅 represents a function or not.

  • Ayes
  • Bno

Q2:

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

  • A π‘₯ = 𝑦 2
  • B 𝑦 = βˆ’ 3 π‘₯ + 6 2
  • C 𝑦 = Β± √ π‘₯
  • D 𝑦 = 8 π‘₯
  • E 𝑦 = βˆ’ 3 π‘₯ βˆ’ 6 2

Q3:

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

Q4:

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

Q5:

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

  • AIt does.
  • BIt does not.

Q6:

Given that π‘₯ and 𝑦 are real variables, which of the following relations is a function of π‘₯ ?

  • A 𝑦 = 8 π‘₯ βˆ’ 4 4 2
  • B 𝑦 = 8 π‘₯ βˆ’ 4 π‘₯ 2 t a n c o s
  • C 𝑦 + π‘₯ = 6 4 2 2
  • D 𝑦 = 8 π‘₯ βˆ’ 4 π‘₯ t a n c o s
  • E 8 𝑦 = βˆ’ 4 𝑦 βˆ’ 8 π‘₯

Q7:

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

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

Q8:

Which of the following relations represents a function?

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

Q9:

, , and is a relation from to . If and , which of the following relations represents a function?

  • A is twice
  • B
  • C is twice
  • D is a factor of
  • E an odd number

Q10:

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

Q11:

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

Q12:

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

  • Ayes
  • Bno

Q13:

If 𝑋 = { 5 , 4 , 8 } , π‘Œ = { 4 9 , 1 6 , 6 4 } , and 𝑅 is a relation from 𝑋 to π‘Œ , where π‘Ž 𝑅 𝑏 means π‘Ž = √ 𝑏 ; π‘Ž ∈ 𝑋 and 𝑏 ∈ π‘Œ , does 𝑅 represent a function?

  • Ano
  • Byes

Q14:

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

  • Aone point
  • Btwo or more points

Q15:

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

  • Ayes
  • Bno

Q16:

Given that 𝑋 = { βˆ’ 7 , 7 , 3 } , π‘Œ = { 5 8 , 1 3 , 𝑙 } , and π‘Ž 𝑅 𝑏 is represented by the equation 𝑏 = π‘Ž + 9 2 , where 𝑅 is a function from 𝑋 to π‘Œ , for which π‘Ž ∈ 𝑋 and 𝑏 ∈ π‘Œ , determine the value of 𝑙 .

Q17:

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

Q18:

Given that 𝑋 = { 1 6 , 8 , 2 0 } , π‘Œ = { 1 3 , 7 } , and 𝑅 = { ( 1 6 , 1 3 ) , ( 8 , 1 3 ) , ( π‘Ž , 1 3 ) } , where 𝑅 is a function from 𝑋 to π‘Œ , find the numerical value of π‘Ž .