# Worksheet: Recognizing Functions from Graphs

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

Q1:

Does the given graph represent a function?

• Ayes
• Bno

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