# 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 Relation B (4,12) (4,15) (5,18) (5,21) (6,24) (4,12) (5,15) (6,18) (7,21) (8,24)
• 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 and output ?

Relation A
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682048
Relation B
07
682048
• 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 , , and is the relation from to , where means , determine whether represents a function or not.

• Ayes
• Bno

Q7:

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

• A
• B
• C
• D
• E

Q8:

Suppose and . How many different functions are there from to ?

Q9:

Suppose and . How many different functions are there from to ?

Q10:

If , and means that is divisible by 5, where is a relation on , determine whether represents a function where and .

• AIt does not.
• BIt does.

Q11:

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

• A
• B
• C
• D
• E

Q12:

Suppose and is a set with elements. How many different functions are there from to ?

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

Q13:

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

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

Q14:

Suppose and . How many different functions are there from to ?

Q15:

Given that , , and , where is a relation from to , does represent a function?

• Ano
• Byes

Q16:

If , , and is a relation from to , where means ; and , does represent a function?

• Ayes
• Bno

Q17:

Given that , , and is represented by the equation , where is a function from to , for which and , determine the value of .

Q18:

Suppose and . How many different functions are there from to ?

Q19:

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

• A
• B
• C
• D

Q20:

Let . Is a function?

• Ano
• Byes

Q21:

Given that , , and , where is a function from to , find the numerical value of .

Q22:

Which of the following is the equation expressed in function notation?

• A
• B
• C
• DThis cannot be expressed as a function.
• E

Q23:

Which of the following relations represents a function from to ? • A
• B
• C
• D

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