# (c) What is a function? Explain different types of functions with example.

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A function is a mathematical concept that describes a relation between a set of inputs and a set of possible outputs, such that each input is related to exactly one output. In simpler terms, a function assigns each element from one set (the domain) to exactly one element in another set (the codomain).

There are different types of functions, and here are some common types:

1. Linear Function:

- Definition: A function that can be represented by a linear equation, typically in the form $$f(x) = mx + b$$, where $$m$$ and $$b$$ are constants.

- Example: $$f(x) = 2x + 3$$ is a linear function.

- Definition: A function that can be represented by a quadratic equation, typically in the form $$f(x) = ax^2 + bx + c$$, where $$a$$, $$b$$, and $$c$$ are constants.

- Example: $$f(x) = x^2 - 4$$ is a quadratic function.

3. Exponential Function:

- Definition: A function where the variable is an exponent. It is often written as $$f(x) = a^x$$, where $$a$$ is a constant.

- Example: $$f(x) = 2^x$$ is an exponential function.

4. Trigonometric Function:

- Definition: Functions involving trigonometric ratios (sine, cosine, tangent, etc.) of an angle.

- Example: $$f(x) = \sin(x)$$ is a trigonometric function.

5. Piecewise Function:

- Definition: A function that is defined by different formulas for different ranges of the input.

- Example:

$f(x) = \begin{cases} x, & \text{if } x < 0 \\ x^2, & \text{if } x \geq 0 \end{cases}$

These are just a few examples, and there are many other types of functions, each serving different mathematical purposes.