Introduction to examples of functions:
A function is a special type of relation. In a function, no two ordered pairs can have the same initial element and a different second element. That is, for a function, corresponding to each first element of the ordered pairs, there must be a different second element. i.e. In a function we cannot have ordered pairs of the form (a1, b1) and (a2, b2) with a1 = a2 and b1 ? b2.
Types of functions:(examples of functions)
1. Onto function
2. One-to-one function:
3. Identity function:
4. Constant function
5. Linear function:
6. Trigonometrical functions:
Explanation of Types of functions: examples of functions
1. Onto function
If the range of a function is equal to the co-domain then the function is
called an onto function. Otherwise it is called an into function.
Definition: A function f is onto if to each element b in the co-domain, there is
at least one element a in the domain such that b = f(a)
Example for Onto function
2. One-to-one function:
A function is said to be one-to-one if each element of the range is
associated with exactly one element of the domain.
i.e. two different elements in the domain (A) have different images in the
co-domain (B).
Note: (1) A function is said to be injective if it is one-to-one.
(2) It is said to be injective if it is both one-to-one and onto.
Example for one to one function:
3. Identity function:
A function f from a set A to the same set A is said to be an identity
function if f(x) = x for all x e A i.e. f : A ? A is defined by f(x) = x for all
x e A. Identity function is denoted by IA or simply I. Therefore I(x) = x always.
Example of Identity function:
f(x) = x
Understanding Absolute Value Piecewise Functions is always challenging for me but thanks to all math help websites to help me out.
4. Constant function:
If the range of a function is a singleton set then the function is called a
constant function.
Example for constant function:
If
f(x) = 8
then
f (13) = 8
Here f is called the constant function. Whatever comes in to f, the number 8 comes out.
5. Linear function:
If a function f : R ? R is defined in the form f(x) = ax + b then the function
is called a linear function. Here a and b are constants.
6. Trigonometrical functions:
In Trigonometry, we have two types of functions.
(1) Circular functions (2)Hyperbolic functions.
We will discuss circular functions only. The circular functions are
Examples of trigonometrical functions are:
(a) f(x) = sinx (b) f(x) = cos x (c) f(x) = tan x
(d) f(x) = secx (e) f(x) = cosecx (f) f(x) = cotx
A function is a special type of relation. In a function, no two ordered pairs can have the same initial element and a different second element. That is, for a function, corresponding to each first element of the ordered pairs, there must be a different second element. i.e. In a function we cannot have ordered pairs of the form (a1, b1) and (a2, b2) with a1 = a2 and b1 ? b2.
Types of functions:(examples of functions)
1. Onto function
2. One-to-one function:
3. Identity function:
4. Constant function
5. Linear function:
6. Trigonometrical functions:
Explanation of Types of functions: examples of functions
1. Onto function
If the range of a function is equal to the co-domain then the function is
called an onto function. Otherwise it is called an into function.
Definition: A function f is onto if to each element b in the co-domain, there is
at least one element a in the domain such that b = f(a)
Example for Onto function
2. One-to-one function:
A function is said to be one-to-one if each element of the range is
associated with exactly one element of the domain.
i.e. two different elements in the domain (A) have different images in the
co-domain (B).
Note: (1) A function is said to be injective if it is one-to-one.
(2) It is said to be injective if it is both one-to-one and onto.
Example for one to one function:
3. Identity function:
A function f from a set A to the same set A is said to be an identity
function if f(x) = x for all x e A i.e. f : A ? A is defined by f(x) = x for all
x e A. Identity function is denoted by IA or simply I. Therefore I(x) = x always.
Example of Identity function:
f(x) = x
Understanding Absolute Value Piecewise Functions is always challenging for me but thanks to all math help websites to help me out.
4. Constant function:
If the range of a function is a singleton set then the function is called a
constant function.
Example for constant function:
If
f(x) = 8
then
f (13) = 8
Here f is called the constant function. Whatever comes in to f, the number 8 comes out.
5. Linear function:
If a function f : R ? R is defined in the form f(x) = ax + b then the function
is called a linear function. Here a and b are constants.
6. Trigonometrical functions:
In Trigonometry, we have two types of functions.
(1) Circular functions (2)Hyperbolic functions.
We will discuss circular functions only. The circular functions are
Examples of trigonometrical functions are:
(a) f(x) = sinx (b) f(x) = cos x (c) f(x) = tan x
(d) f(x) = secx (e) f(x) = cosecx (f) f(x) = cotx
