Differential Calculus: Functions - Lecture Notes, Summaries of Calculus

Download Differential Calculus: Functions - Lecture Notes and more Summaries Calculus in PDF only on Docsity!

Differential Calculus

Math 201

“ Functions”

Lecture 2

Mr.Abdullah Alghamdi 1

What will be discussed :

1. Function 2 .Domain and range.
2. Vertical Line Test. 4 .Symetry of Function. 5 .Increasing and Decreasing.

Functions Definition :

• The number f(x) is the value of f at x and is read “ f of x .”

Table representing a function

7

Quadratic Function : f(x) =x 2 8 F(x)=x 2 is called Quadratic function

The Vertical Line Test

It is not a function

It is a function

11

Range of Function :

• The Range of a function ,f, consists of all possible outputs ( things you might receive from f ) or the set of all values of f as x varies throughout the domain.

If f is a function with domain D , then its graph is the set of

ordered pairs {(^ x f ,^^ (^ x^ ))^ x^  D }

Domain For Real valued Functions : If you have a function that has not been determined its domain; The domain of any real function is R except 3 functions: Fractions, Root and Logarithm function. 17

Constant Function : 19

Identity Function : f(x) = x 20 F(x)=x is called identity function