In mathematics, the functions are used to identify the varying quantity with respect to other quantity. It is represented as f(x). In other words, the function is a relation in which each element in a domain is exactly associated with one element of a co-domain. Functions have various inputs and outputs which are represented in many ways. They are:
The functions in mathematics are important because the theories about dependencies between two quantities are developed. There are different types of functions in mathematics such as
- Algebraic function
- Constant function
- Polynomial function
- Linear function
- Logarithmic function
- Quadratic function
- Cubic Function
- Trigonometric function
The function which is defined using algebraic expressions is called algebraic functions.
Example: f(x) = x2 + x + 2
If X and Y are the two non-empty sets, then the function from X to Y is called constant function iff the range of “f” is a singleton set.
The polynomial function of degree “n” is of the form P(X) = anxn + an-1xn-1+….+a1x +a0 where “n” is a positive integer and an, an-1,….a1, a0 are the real numbers.
Example: x2 – 4x + 7
The linear function is a polynomial function that has one independent variable and one dependent variable. The general form of a linear function is
f(x) = ax +b
Example: y = 25 + 5x
The function which appears as an argument of a logarithm is called logarithmic function. The general form of a logarithmic function is
f(x) = loga(x)
Example: f(x) = log sin (x)
The quadratic function is defined as the polynomial equation of degree “2” and is of the form
f(x) = ax2 + bx + c
Example: x2 + 5x + 6
The polynomial function with highest degree of “3” is called cubic function with general form
f(x) = ax3 +bx2+cx+d
Example: 2x3 +3x – 6
The function in which an angle is represented as the ratio of two sides of a right-angled triangle is called trigonometric functions.
Example: f(x) = sin x, f(x)= cos x, f(x) = tanx etc.
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