In mathematics, a variable is represented by a symbol that can be changed according to the problem. The common symbols used to represent variables are \(x\), \(y\), and \(z\).
In mathematics, a constant is a fixed and known value that can not be changed, commonly constants are represented by numbers and symbols \(a\), \(b\), and \(c\).
Example: \(2x + y = 25\)
Here \(x\), and \(y\) are variables whereas 2 and 25 are constants.
The expression made by using variables and constants with the help of operators (+, -, \(\times\), \(\div\)) is called an algebraic expression.
Example: \(ax^2 + bx + c\)
Here a, b, and c are constants, and \(x\) is a variable.
An algebraic expression is called an algebraic function of a variable (\(x, y, z\)) and it is commonly represented by \(f(x)\), \(f(y)\), \(f(z)\) etc.
Example: \(f(x) = 2x^2 + 3x + 1\)
It is an algebraic expression with finite terms and for each term, the exponent of the variable should be positive.
Example: \(3x^2 + 2x + 1\)
Here 1, 2, and 3 are constants whereas \(x^2\) and \(x\) are variables with positive exponents.
A rational function is the ratio of two polynomials where denominator cannot be zero.
Example: \(f(x) = \frac{x^2 + 2}{x^2 + 1}\)
Here \(x^2 + 1\) can not be equal to zero.