FUNCTIONS group 551109_14

FUNCTIONS

Created by: group 551109_14

Differential calculus course

Definition:

In maths, a function is a relationship between two sets, output set and input set. If A and B are any two sets, then a function from A to B is a rule that assigns to each element of A exactly one element of B. In other words, if A and B are two sets, then a function from A to B is a set f of ordered pairs in A x B with the property that for each a ∈A there exists a unique b ∈B with (a,b)∈f.

FUNCTIONS

Created by: group 551109_14

Differential calculus course

Algebraic functions

Transcendent functions

Includes the trigonometric, inverse trigonometric, exponential and logarithmic functions, and also includes other functions.

FUNCTIONS

Created by: group 551109_14

Differential calculus course

Transcendent function

Subtítulo

Transcendent function

Classification according to simmetry

FUNCTIONS

Created by: group 551109_14

Differential calculus course

Classification according to variable expression

Explicit function The function can be expressed as an equation in terms of one variable.

Implicit function Is a function with multiple variables and one of the variables is a function of the other set of variables.

Classification according to continuity

FUNCTIONS

Created by: group 551109_14

Differential calculus course

Classification according to relationship between domain and range

Inyective function: A function f is injective if and only if whenever f(x) = f(y), x = y.

Surjective function: A function f (from set A to B) is surjective if and only if for every y in B, there is at least one x in A such that f(x) = y, in other words f is surjective if and only if f(A) = B.

Bijective function: A function f (from set A to B) is bijective if, for every y in B, there is exactly one x in A such that f(x) = y