# 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 |

- 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.

**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