Function

Definition of Function

• Function is a relation in which each element of the domain is paired with exactly one element of the range.

Example of Function

• f(x) = x + 4, , f(s) = 7s are few examples of function.

More about Function

• A function is a relationship between two quantities in which one quantity depends on the other.
• A function is a many-to-one (or sometimes one-to-one) relation.

Solved Example on Function

Brad sells a vacuum cleaner and earns $4 as commission for each vacuum cleaner he sells. The owner pays him depending on how many vacuum cleaners he sells. Identify the table that best suits the situation, also plot a graph for the input - output table.

Choices:

A. Table 1

B. Table 2

C. Table 3

D. None of the above

Correct Answer: A

Solution:

Step 1: The commission earned by Brad on each vacuum cleaner

he sells = $4.

Step 2: The amount earned by Brad (a) = 4 x number of vacuum cleaners he sells (n).

Step 3: a = 4n                [Original equation.]

Step 4: a = 4(0) = 0       [Substitute 0 for n and simplify.]

Step 5: a = 4(3) = 12      [Substitute 3 for n and simplify.]

Step 6: a = 4(5) = 20     [Substitute 5 for n and simplify.]

Step 7: a = 4(7) = 28     [Substitute 7 for n and simplify.]

Step 8: a = 4(10) = 40   [Substitute 10 for n and simplify.]

Step 9: a = 4(12) = 48   [Substitute 12 for n and simplify.]

Step 10: Among the choices, Table 1 satisfies the equation.

Step 11: The graph below represents the function a = 4n.

                       

Related Terms for Function

• Domain
• Range
• Relation
• Element

Additional Links for Function

• Click here for samples
• Back to Mathematics Dictionary