Lesson Worksheet: Identifying Functions Mathematics

In this worksheet, we will practice identifying a function from a relation shown by a set of ordered pairs, a relation diagram, an equation, or a graph.


What is a function?

  • AA dependent quantity
  • BA combination of domain and range
  • CA relation that relates each input to exactly one output
  • DAn independent quantity


True or False: The following set of ordered pairs represents a function: {(1,3),(2,6),(3,9),(4,12)}.

  • ATrue
  • BFalse


Which of these sets of ordered pairs does not represent a function?

  1. {(1,2),(2,4),(3,6),(4,8)}
  2. {(1,2),(2,4),(3,6),(3,8)}
  3. {(2,10),(3,15),(4,20),(5,25)}
  4. {(2,10),(2,15),(4,20),(4,25)}
  • Ab and d
  • Bc
  • Cb and c
  • Da and d
  • Eb


Which of the following relations represents a function?

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


Which of the following relations represents a function?

Relation A(4,12)(4,15)(5,18)(5,21)(6,24)
Relation B(4,12)(5,15)(6,18)(7,21)(8,24)
  • ARelation A
  • BRelation B


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

  • AAt most one.
  • BTwo or more points.


Does the given graph represent a function?

  • ANo
  • BYes


Which of the following relations represents a function given that 𝑥 is the input and 𝑦 is the output?

  • A(a)
  • B(b)


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

  • A𝑓(𝑥)=𝑥+1
  • B𝑓(𝑦)=𝑥+1
  • C𝑓(𝑥)=𝑥+1
  • DThis cannot be expressed as a function.
  • E𝑓(𝑥)=𝑥+1


Can the equation 𝑥+𝑦=4 be expressed as a function? If yes, state the function.

  • AYes, 𝑓(𝑥)=2𝑥
  • BYes, 𝑓(𝑥)=±2𝑥
  • CYes, 𝑓(𝑥)=±4𝑥
  • DNo
  • EYes, 𝑓(𝑥)=4𝑥

This lesson includes 24 additional questions and 117 additional question variations for subscribers.

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