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1. Functions
Input, output, relationship, equation, variables

2. 1 2
Learning Outcomes
Represent real-life
situations using
both verbal
descriptions and
mathematical
functions.
Identify and apply
two different types
of functions to
model relationships
between variables.

3. Warm-Up
📌 Think-Pair-Share Activity:
Look at these two statements:
1. The total cost of apples depends on how many kilograms you buy.
2. The distance traveled depends on the speed and time.
Discuss with a partner:
What is changing in each situation?
Can you express this relationship using a mathematical function?

4. 📌 Think-Pair-Share Activity:
Look at these two statements:
1. The total cost of apples depends on how many kilograms you buy.
Changing quantity: (Independent variable): Kilograms of apples (let's call it x)
Dependent variable: Total cost (let's call it y)
Function:
2. The distance traveled depends on the speed and time.
Changing quantity: (Independent variable): Speed (s) and Time (t)
Dependent variable: Distance traveled (d)
Function:

5. Function in Real Life
How do machines know how much to charge or what speed a car is moving?
Why does a vending machine give a soda when you press a specific button?

6. Function in Real Life
Functions are rules that relate one quantity (input) to another quantity (output).
In real life, many things follow a functional relationship:
 Speed depends on time traveled.
 The cost of groceries depends on the number of items bought.
 The height of water in a tank depends on the time it has been filling.

7. Understanding Functions
A function is a rule that assigns each input (x) to exactly one output (y).Functions
express relationships between quantities.
Real-Life Example:
Fatima buys pencils and pens. The total cost depends on the number of each
item she buys.
c= Number of pencils k= Number of pens
Each pencil costs $2, each pen costs $6, and the total cost is $30.
Key Understanding:
A function can be written in words or as an equation. The function must make
logical sense in the given context.

8. Implicit Functions
Some functions are not written in the standard y = mx + c form but still
express a relationship.
Example 1:
Ali and Bella have $37 in total.
Equation:
Interactive Question:
Answer: B

9. Worked Example
 Situation: Fatima buys pencils at $2 each and pens at $6 each. She spends $30.
Equation:
Step-by-Step Explanation:
1. If Fatima buys 0 pencils, how many pens can she buy?
2. If she buys 3 pencils, how many pens can she buy?
3. If she buys 6 pencils, how many pens can she buy?
 Completed Table of Values:
c (pencils) k (pens)
0 5
3 4
6 3
9
12
15

10. Worked Example
 Completed Table of Values:
 Discussion Question:
If Fatima buys 3 pencils and 4 pens, does this satisfy the equation?
Check by substituting values into .
c (pencils) k (pens)
0 5
3 4
6 3
9 2
12 1
15 0

11. Practice Questions
1. A car rental company charges a base fee of $10 plus $5 per hour.
o Write an equation for the total cost, C, after h hours.
2. A farmer sells apples for $3 each and oranges for $4 each.
o Write an equation for the total cost of buying a apples and o oranges.
3. A school has boys and girls, and the total number of students is 200.
o Write an equation to represent the number of boys (b) and girls (g).

12. Practice Questions
4. The cost of a taxi ride is $4 per kilometer plus a $6 fixed fee.
o Write an equation to represent this situation.
5. A company sells small and large t-shirts. Small t-shirts cost $10 each, and
large t-shirts cost $15 each. The company made $500 in sales.
o Write an equation to represent this.

13. Steps to Represent a Function
o Identify the Variables: Determine what is changing in the situation and assign variables
to represent these quantities (e.g., x for input, y for output).
o Understand the Relationship: Recognize how the variables are related. Is it a direct
relationship (e.g., cost per item) or dependent on multiple factors (e.g., speed × time)?
o Write the Function: Express the relationship between the variables using a mathematical
function (e.g., ).
o Interpret the Function: Understand what the function represents in real life. For
example, in , x represents the number of tickets, and y represents the total cost.
o Solve Using the Function: Substitute known values into the function to find unknown
quantities (e.g., calculate the cost for different numbers of tickets).
o Check the Solution: Verify that your function and results make sense in the context of the
situation.