Function in Mathematics

Function in Mathematics

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  WELCOME TO PRESENTATION
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  Presentation On: Function SubmittedTo: MD. ARIFUZZAMAN (AZ) Lecturer in Mathematic, Department of Natural Sciences Submitted By: MD. MAHABUB JAHAN ID: 142-15-4054
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  Slide overview  Function Some features of function  Variation of Function  Explain of function  Interval  Domain:  Use of Function
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  Function  Let, Xand 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.
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  Some features offunction  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
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   Onto function: Afunction 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
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  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
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  3. Exponential function Example:y=𝑒 𝑥 4. Logarithmic function Example: y=logx
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  Explain of function y=f(x) y is a function of x. Where y is a dependent variable and x is an independent variable.
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  Interval  ( )→𝑂𝑝𝑒𝑛 𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙 Ex: 1< 𝑥 < 5 (1, 5)  [ ]→ 𝐶𝑙𝑜𝑠𝑒 𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙 Ex: 1≤ 𝑥 ≤ 5 [1, 5]
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  Domain: • There aretwo kinds of Domain. 1. Natural Domain Y=f(x), Df=ℝ 2. Restricted Domain y=x, Df= 0, ∞
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  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.