Introduction to Function Notation

Function Notation Explained

Introduction to Function Notation

• The video introduces the concept of function notation, defining a function f from set A to set B .

• A function assigns each element in the domain (set A ) exactly one element in the codomain (set B ).

Domain and Codomain

• The domain is defined as all possible inputs (elements of set A ), while the codomain consists of potential outputs (elements of set B ).

• An example is provided with sets: let A = 1, 2, 3 and B = 3, 4, 5, 6 .

Example Function Definition

• The function is defined by specific mappings:

• f(1) = 3

• f(2) = 4

• f(3) = 5

• It’s emphasized that no input can map to multiple outputs; otherwise, it would not be a valid function.

Real Numbers and Quadratic Functions

• Another example involves defining a function from real numbers to real numbers using the equation f(x) = x^2 .

• This quadratic function produces a parabola when graphed, illustrating how inputs relate to outputs.

Range and Co-domain Clarification

• The range of this quadratic function is discussed as being from bracket [0, ∞), indicating all possible output values.

• It’s noted that the co-domain can be larger than the domain without affecting the validity of the function.