Worksheet: Relations and Functions

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 , 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 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 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 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 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=116,18,14,12,1,2,4,8, and 𝑅 is the relation from 𝑋 to 𝑌, where 𝑎𝑅𝑏 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 𝑦 = 3 𝑥 6
  • B 𝑦 = 8 𝑥
  • C 𝑥 = 𝑦
  • D 𝑦 = ± 𝑥
  • E 𝑦 = 3 𝑥 + 6

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={𝑥𝑥,1𝑥4}, and 𝑎𝑅𝑏 means that 𝑎+𝑏 is divisible by 5, where 𝑅 is a relation on 𝑋, determine whether 𝑅 represents a function where 𝑎𝑋 and 𝑏𝑋.

  • AIt does not.
  • BIt does.

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

Q12:

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

  • A 𝑛 + 1
  • B 𝑛
  • C
  • DIt is not possible to say.
  • E1

Q13:

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

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

Q14:

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

Q15:

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

  • Ano
  • Byes

Q16:

If 𝑋={5,4,8}, 𝑌={49,16,64}, and 𝑅 is a relation from 𝑋 to 𝑌, where 𝑎𝑅𝑏 means 𝑎=𝑏; 𝑎𝑋 and 𝑏𝑌, does 𝑅 represent a function?

  • Ayes
  • Bno

Q17:

Given that 𝑋={7,7,3}, 𝑌={58,13,𝑙}, and 𝑎𝑅𝑏 is represented by the equation 𝑏=𝑎+9, where 𝑅 is a function from 𝑋 to 𝑌, for which 𝑎𝑋 and 𝑏𝑌, determine the value of 𝑙.

Q18:

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

Q19:

In which of the following relations is 𝑦 NOT a function of 𝑥?

  • A 𝑥 = 𝑦 1 8
  • B 𝑦 = 5 4 𝑥 + 5 0
  • C 𝑦 = 𝑥 6 5
  • D 𝑦 = 5 4 𝑥 + 5 0

Q20:

Let 𝑓={(𝑎,1),(𝑏,3),(𝑐,1)(𝑑,3)}. Is 𝑓 a function?

  • Ano
  • Byes

Q21:

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

Q22:

Which of the following is the equation 𝑦=𝑥+1 expressed in function notation?

  • A 𝑓 ( 𝑥 ) = 𝑥 + 1
  • B 𝑓 ( 𝑦 ) = 𝑥 + 1
  • C 𝑓 ( 𝑥 ) = 𝑥 + 1
  • DThis cannot be expressed as a function.
  • E 𝑓 ( 𝑥 ) = 𝑥 + 1

Q23:

Which of the following relations represents a function from 𝑋 to 𝑌?

  • A ( 𝑅 2 )
  • B ( 𝑅 1 )
  • C ( 𝑅 4 )
  • D ( 𝑅 3 )

Q24:

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

  • ATrue
  • BFalse

Q25:

Which of the following relations represents a function?

  • ARelation B
  • BRelation A

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