Functions IIT Questions NO 03 ( X Class)

In mathematics, a function is a relation between two sets of numbers, known as the domain and the range. The domain represents all possible inputs to the function, while the range represents all possible outputs. A function maps each input in the domain to a unique output in the range.

Functions can be represented using mathematical notation, such as f(x) or g(y), where x and y are variables that represent the input to the function, and f(x) and g(y) are the corresponding output values.

Functions can be classified into various types based on their properties, such as:

Linear functions: These are functions of the form f(x) = mx + b, where m and b are constants. They have a constant rate of change and produce a straight line when graphed.

Quadratic functions: These are functions of the form f(x) = ax^2 + bx + c, where a, b, and c are constants. They have a parabolic shape when graphed.

Exponential functions: These are functions of the form f(x) = a^x, where a is a constant. They grow exponentially and have an asymptotic curve when graphed.

Trigonometric functions: These are functions of the form f(x) = sin(x), cos(x), or tan(x), where x is an angle in radians. They represent periodic oscillations and have a repeating pattern when graphed.

Functions are used in many areas of mathematics and applied sciences, including calculus, statistics, physics, and engineering. They are also used in computer programming to represent algorithms and data structures.

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