Chapter 2 Functions
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Project on Mathematics
In mathematics, a function is a rule or relationship that
assigns each input value from a set (called the domain) to exactly one output
value from another set (called the codomain or range).
Let's break this down:
1. Input: This is the value you plug
into the function. It's also known as the independent variable.
2. Output: This is the value that the
function produces after you've plugged in the input. It's also known as the
dependent variable.
3. Rule or Relationship: This defines how the input
values are related to the output values. It can be expressed in various ways,
such as algebraic formulas, graphs, tables, or verbal descriptions.
4. Exactly One Output: Each input value in the
domain should correspond to exactly one output value in the codomain. This
means a function cannot give multiple outputs for a single input.
Functions are often denoted by letters, such as 𝑓(𝑥)
where 𝑓f
is the name of the function and 𝑥x is the input variable.
For example, 𝑓(𝑥)=2𝑥 represents
a function that doubles its input.
Functions are fundamental in mathematics and are used to describe various relationships, model real-world phenomena, and solve problems in diverse fields like physics, economics, engineering, and more.