In this worksheet, we will practice recognizing functions from schematic descriptions, arrow diagrams, and graphs.

**Q2: **

Fady believes that setting equal to the digit before the decimal point in the decimal expansion of , for each real number, defines a function from the real numbers to the set of digits . Since and are both decimal expansions of the real number 1, what does that say about ?

- A defines a function with .
- B defines a function with .
- C defines a function with or 1.
- D does not define a function.
- E defines a function with .

**Q3: **

Let and . Which of the following properties is true of the relation between and given by , where and ?

- A is not a function of because when there is no corresponding value of .
- B is not a function of because cannot always be found.
- C is not a function of because when there is no corresponding value of .
- D is a function of because each input gives a real number whose cube root gives the unique output .

**Q4: **

If is a function from the set to the set , what do we call ?

- A the range of the function
- B the domain of the function
- C the rule of the function
- D the codomain of the function

**Q5: **

If , which of the following arrow diagrams represents a function on the set ?

- A(C)
- B(B)
- C(D)
- D(A)

**Q6: **

If , , and the function , where , which of the sets below can be a representation of ?

- A
- B
- C
- D

**Q7: **

For two sets and , a function exists from to . Also, , , and means is a multiple of . If , , and , determine .

- A
- B
- C
- D
- E

**Q8: **

For two sets and , a function exists from to . Also, , , and means is a multiple of . If , , and , which of the following definitions of and are correct?

- A ,
- B ,
- C ,
- D ,
- E ,

**Q9: **

For two sets and , a function exists from to . Also, , , and means is divisible by . If , , and , find and .

- A ,
- B ,
- C ,
- D ,

**Q10: **

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

- Atrue
- Bfalse

**Q11: **

Can the equation be expressed as a function? If yes, state the function.

- AYes,
- BYes,
- CYes,
- DNo
- EYes,

**Q12: **

What is a function?

- AAn independent quantity
- BA dependent quantity
- CA combination of domain and range
- DA relation that relates each input to exactly one output

**Q13: **

Given that and are variables, determine whether is a function, and if it is, state which equation is equivalent to it.

- AIt is a function,
- B It is a function,
- CIt is a function,
- DIt is not a function.
- EIt is a function,

**Q14: **

Which of the following equations are NOT functions of ?

- Ab and c
- Ba and c
- Ca and d
- Db and d
- Ea and b

**Q15: **

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

- AThis cannot be expressed as a function.
- B
- C
- D
- E

**Q16: **

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

- Afalse
- Btrue

**Q17: **

If is a function from the set to the set , what do we call ?

- A the range of the function
- B the codomain of the function
- C the rule of the function
- D the domain of the function

**Q18: **

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

**Q19: **

What is the codomain of a function?

- Aa set of values that can go into the function
- Ba set of values that actually comes out of the function
- Ca set of values that may possibly come out of or go into the function
- Da set of values in which the outputs of a function are contained
- Ea set of values that actually comes out of or goes into the function

**Q20: **

The figure below shows the graph of a function .

Which of the following *cannot* be the codomain of this function?

- A the set of rational numbers
- B the set of real numbers
- C the interval
- D the set of negative integers
- Ethe numbers such that

**Q21: **

Given that , , , and , find the codomain of the function.

- A
- B
- C
- D

**Q22: **

, , , , and where is a function on . Find the ordered pairs that satisfy the function and its range.

- A , range
- B , range
- C , range
- D , range
- E , range

**Q23: **

Suppose and is a set with 5 elements. How many different functions are there from to ?

**Q24: **

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

- A
- B
- C
- D
- EIt is not possible to say.

**Q25: **

If is a function from the set to the set , which set is the domain of ?

- A
- B
- C
- D