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Lesson: Determining Whether a Relation Is a Function

Sample Question Videos

Worksheet • 18 Questions • 1 Video

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 A
  • BRelation B

Q2:

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

  • AA function is a mathematical rule that assigns to each input more than one output.
  • BA function is a relation that assigns to each input exactly 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
𝑋 βˆ’ 3 0 3 8 βˆ’ 1 0
π‘Œ 6 8 20 4 8
Relation B
𝑋 βˆ’ 2 0 βˆ’ 2 7 βˆ’ 8
π‘Œ 6 8 20 4 8
  • ARelation B
  • BRelation A

Q4:

Which of the following relations represents a function?

  • A (c)
  • Ball
  • C (a) and (c)
  • D (b)
  • E (a)

Q5:

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

  • Atwo or more points
  • Bone point

Q6:

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.

  • Ano
  • Byes

Q7:

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

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

Q8:

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

Q9:

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

Q10:

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 not.
  • BIt does.

Q11:

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

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

Q12:

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

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

Q13:

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

  • A π‘Ž is a factor of 𝑏
  • B π‘Ž βˆ’ 2 𝑏 = an odd number
  • C π‘Ž + 𝑏 < 8
  • D 𝑏 is twice π‘Ž
  • E π‘Ž is twice 𝑏

Q14:

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

Q15:

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?

  • Ano
  • Byes

Q16:

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?

  • Ayes
  • Bno

Q17:

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 .

Q18:

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

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