FUNCTION
Definition Of Function
Function is a relation in which each element of the domain is paired with exactly one element of the range.
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.
Video Examples: iCoachMath works
Example of Function
f(x) = x + 4, 
, f(s) = 7s are few examples of function.
Solved Example on Function
Ques: 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.
Quick Summary
- A function is a relationship between two quantities where one depends on the other.
- Functions can be many-to-one or one-to-one relations.
🍎 Teacher Insights
Use real-world examples to illustrate functions (e.g., vending machines, input-output machines). Emphasize the vertical line test to visually determine if a graph represents a function.🎓 Prerequisites
- Relations
- Sets
- Domain
- Range
Check Your Knowledge
Q1: Which of the following relations is a function?
Q2: If f(x) = x + 4, what is f(3)?
Frequently Asked Questions
Q: What is the difference between a relation and a function?
A: A function is a special type of relation where each input has only one output.
Q: Can a function have the same output for different inputs?
A: Yes, a function can have multiple inputs that map to the same output (many-to-one).