This document is a presentation on mathematical functions, detailing their features, variations, and applications. It covers concepts such as even and odd functions, one-one and onto functions, and types of functions including algebraic, trigonometric, exponential, and logarithmic. Additionally, it discusses the concept of intervals and domains, and the use of functions in programming and various industries.

1. WELCOME
TO
PRESENTATION

2. Presentation On: Function
Submitted To:
MD. ARIFUZZAMAN (AZ)
Lecturer in Mathematic, Department
of Natural Sciences
Submitted By:
MD. MAHABUB JAHAN
ID: 142-15-4054

3. Slide overview
 Function
 Some features of function
 Variation of Function
 Explain of function
 Interval
 Domain:
 Use of Function

4. Function
 Let, X and Y are two on empty set.
 A formula/rule establishing relation between the numbers of X
and Y.
 It assigns each value of X to each value of Y then f is called a
Function.

5. Some features of function
 Even and odd function:
If f(-x)=f(x), so f(x) is call even function.
If f(x)=f(x), so f(x) is called odd function.
One-one function:
f(x1)=f(x2), if x1=x2
f(x1)=f(x2), if x1≠
x2

6.  Onto function:
A function f:x→ 𝑌 a set to be onto function if for
every y∈Y there is a value x∈ 𝑋such that f(x)=y
Onto Function Not onto Function

7. Variation of Function
1. Algebraic function
Algebraic function are two kinds of
*Polynomial function
Ex: y=x2+5x-9
*Rational function
Ex: R(x) =
𝑝(𝑥)
𝑞(𝑥)
, 𝑞 𝑥 ≠ 0
2. Trigonometric function
Example: y=sin 𝑥

8. 3. Exponential function
Example: y=𝑒 𝑥
4. Logarithmic function
Example: y=logx

9. Explain of function
 y=f(x)
y is a function of x. Where y is a dependent variable and x is an
independent variable.

10. Interval
 ( )→ 𝑂𝑝𝑒𝑛 𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙
Ex: 1< 𝑥 < 5 (1, 5)
 [ ]→ 𝐶𝑙𝑜𝑠𝑒 𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙
Ex: 1≤ 𝑥 ≤ 5 [1, 5]

11. Domain:
• There are two kinds of Domain.
1. Natural Domain
Y=f(x), Df=ℝ
2. Restricted Domain
y=x, Df= 0, ∞

12. Use of Function:
• We use function in Programming Language to create program or
software just like C/C++.
• We can solve many difficult mathematics by using Function.
• Many Industry, Bank and other organization use function for many
reason.