Please enable JavaScript.
Coggle requires JavaScript to display documents.
FUNCTIONS, TYPES OF FUNCTIONS, GRAPHS OF FUNCTIONS, 1200px-Domain,_Range,…
FUNCTIONS
Domain
f: A → B denotes that f is a function from A to B, where A is a domain.
Any element in the domain must be related to only one element in the range.
Every element in the domain is related with an element in the range.
Range
The set of all images of all x’s is a subset of set B (codomain) and is called an range.
Codomain (Image)
f: A → B denotes that f is a function from A to B, where B is a co-domain. Image of A under f is shown as f(A).
TYPES OF FUNCTIONS
Into Function
If at least set B has a element which is not connected with any of the element of set A.
Onto (Surjective) Function
If each element of the codomain is mapped to by at least one element of the domain it is called as onto function. In other words, each element of the codomain has non-empty preimage. Equivalently, a function is surjective if its image is equal to its codomain.
One to One Function
If the image of each element in the domain is different than one another, the function is called a one-to-one function.
Identitiy Function
The function f is called the identity function if each element of set A has an image on itself.
.A → A such that. f = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5)}.
Constant Function
If f maps all the elements of set A to one and only one element of set B, this function is called as a constant function and is denoted by f(x) = c where c is a constant real number.
Linear Function
Linear functions are those whose graph is a straight line. A linear function has the following form.
Piecewise Function
If a function can’t be described by a single equation, and instead we have to describe it using a combination of equations it is called as a piecewise function.
Equal Function
The domain and the range of the functions must be equal. The image of each element of the domain under both functions must be equal.
If f is a linear function, then its graph is a line.
GRAPHS OF FUNCTIONS
