Functions and Graphs (lecture 1)

1.

Lecture 1. Functions and Graphs
(part 1)
Lecturer : Askar Maulenov, PhD,
associate professor
Askar Maulenov

2.

Content
• Definition of function. Examples
• Forms of representing a function
• The domain of a function.
• Even and odd functions. Examples
• Functions defined in pieces
• Composite functions
• Inverse functions
• Classification of functions
Askar Maulenov

3.

Definition of function.
Definition
If to each value of the variable x (independent variable within a
certain range) there corresponds one definite value of another
variable y (dependent variable) ,
then y is a function of x: y = f(x).
We read as “y equals f of x.”
Standard notations :
,
Askar Maulenov

4.

Definition of function.
Askar Maulenov

5.

Diagram Illustration.
Askar Maulenov

6.

Examples of function.
The values of one variable often depend on the values for
another:
• The temperature at which water boils depends on elevation
(the boiling point drops as you go up due to decreasing
atmospheric pressure).
• The amount by which your savings will grow in a year
depends on the interest rate offered by the bank and the
time.
• The position of the point performing harmonic oscillations
depends on time
Askar Maulenov

7.

Examples of function : The temperature at which
water boils depends on elevation
Askar Maulenov

8.

Examples of function : the amount of your
savings will grow in a year
Askar Maulenov

9.

Examples of function : position of a point
performing harmonic oscillations, over time
Askar Maulenov

10.

Forms of representing a function
1) Analytical
The function is defined using a formula that expresses the
relationship between the variable