General Mathematics

1. Lesson 1
Functions,
Function Notations, and
Equations

2. Objective
At the end of this lesson, the learner should be able to
 correctly define a function;
 properly represent a function using function notation;
and
 properly model real-life problems using equations.

3. Essential Questions
 What is a function?
 How will you represent functions?
 How will you determine whether a given equation is a
function?

4. Learn about It!
Function
It is a special kind of relation in which no two distinct ordered pairs have the
same first element.
1
In an equation in two variables, and , the variable may be
expressed as if every value of corresponds to a single value
of .

5. Learn about It!
Independent and Dependent Variables
The value that a function takes in is called the input or the independent variable
while the corresponding value that it produces is the output or the dependent
variable.
2
Example:
Assume that you are in a grocery store. Each grocery item
has its own corresponding price.
This is an example of a function wherein the independent
variable is the grocery item while the dependent variable is
its price.

6. Learn about It!
Ways of Writing Functions
3
Example: There are different ways of writing .
Function Notation Description
is written as a function of , or
The arrow is read as “is mapped to.”
The colon symbol () is read as “such that.”
The function is written as a set.

7. Try It!
Example 1: Consider an electric fan as a function machine.
What you do you think is the input, the function,
and the output?

8. Try It!
Answer:
Pressing any button on the electric fan (assuming it is
plugged into a power source) will cause the fan blade to
spin.
Hence, the buttons are the input, the spinning of the fan
blade is the function, and the wind it gives off is the output.
Example 1: Consider an electric fan as a function machine.
What you do you think is the input, the function,
and the output?

9. Try It!
Example 2: Consider the table of values below. Determine
the input, the function, and the output.

10. Try It!
Solution:
The -values are the input. The -values are the output.
Notice that if the value of is , the value of is . If is , is , and
so on.
Example 2: Consider the table of values below. Determine
the input, the function, and the output.

11. Try It!
Solution:
By observing the pattern, note that each input is doubled
after “going through” the function.
Hence, the function is .
Example 2: Consider the table of values below. Determine
the input, the function, and the output.

12. Let’s Practice!
Individual Practice:
1. Consider a water dispenser as a function machine. What
is the input, the function, and the output?
2. Consider the table of values below. Determine the input,
the function, and the output.

13. Let’s Practice!

14. Key Points
Function
It is a special kind of relation in which no two distinct ordered pairs have the
same first element.
1
Independent and Dependent Variables
The value that a function takes in is called the input or the independent variable
while the corresponding value that it produces is the output or the dependent
variable.
2

15. Key Points
Ways of Writing Functions
3
Function Notation Description
is written as a function of , or
The arrow is read as “is mapped to.”
The colon symbol () is read as “such that.”
The function is written as a set.

16. Synthesis
● How do we denote a function?
● How do we make use of functions in our life?
● What do we call relationships that are not functions?