Lesson-1-Functions-Function-Notations-and-Equations.pdf

Functions-function notations

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. Warm Up!
Subtract your birth month from 12 and add the result in
step 2.

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 inputor the independent variable
while the corresponding value that it produces is the outputor 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 Functions3
Example:There are different ways of writing �=2�+6.
Function Notation Description
��=2�+6 �is written as a function of �, or �(�)
�→2�+6 The arrow is read as “is mapped to.”
�:�→2�+6 The colon symbol (:) is read as “such that.”
�={�,�|�=2�+6}The function �is written as a set.

7. Learn about It!
Piecewise Function
It is a function composed of two or more expressions for the different parts of the
domain.
4
Example:
��=ቐ
3&#3627408485;if&#3627408485;<0
−1if&#3627408485;=0
&#3627408485;
2
if&#3627408485;>0

8. 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?

9. 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?

10. Let’s Practice!
Individual Practice:
1.Consider a water dispenser as a function machine. What is
the input, the function, and the output?

11. Let’s Practice!
Individual Practice:
1.Consider a water dispenser as a function machine. What is
the input, the function, and the output?

12. Let’s Practice!

13. 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 inputor the independent variable
while the corresponding value that it produces is the outputor the dependent
variable.
2

14. Key Points
Ways of Writing Functions3
Function Notation Description
&#3627408467;&#3627408485;=2&#3627408485;+6 &#3627408486;is written as a function of &#3627408485;, or &#3627408467;(&#3627408485;)
&#3627408485;→2&#3627408485;+6 The arrow is read as “is mapped to.”
&#3627408467;:&#3627408485;→2&#3627408485;+6 The colon symbol (:) is read as “such that.”
&#3627408467;={&#3627408485;,&#3627408486;|&#3627408486;=2&#3627408485;+6}The function &#3627408467;is written as a set.
Piecewise Function
It is a function composed of two or more expressions for the different parts of the
domain.
4