Why are Functions Important in Mathematics?
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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