Relations and Functions | Class 11 Mathematics Notes

2.4 Functions

A function is a special type of relation from a set A (domain) to a set B (codomain) where every element of A has exactly one image in B. This means no two ordered pairs in the function have the same first element with different second elements. If f is a function from A to B and (a, b) ∈ f, then f(a) = b, where b is called the image of a under f, and a is called the preimage of b. The function is denoted by f: A → B. The domain of f is A, and the codomain is B. The range is the set of all images of elements in A under f. Examples illustrate that relations where some elements in the domain have no image or have multiple images are not functions. Real valued functions are functions where the domain and range are subsets of real numbers. For example, the function f: N → N defined by f(x) = 2x + 1 is a real valued function with domain N and range the set of odd natural numbers. Functions can be represented by tables, formulas, or graphs. Understanding functions is crucial as they model precise correspondences in mathematics and real-world phenomena.

📊 Diagram: No specific diagrams in this section; relates to previous figures illustrating relations.

🧪 Activity: Students examine relations to determine if they are functions and identify domain, codomain, and range.

🔗 Connection: This section leads to studying specific types of functions and their graphical representations.

Table on page 8 (2×8)

Table on page 8 (2×8)

Table on page 10 (2×10)

Table on page 10 (2×10)

Table on page 11 (2×10)

Table on page 11 (2×10)