A function is a mathematical relationship whether the value of a single dependent variable is determined from the values of one or more independent variables. The given is an example of a function wherein y is said to be a function of x.
y = a + bx
In the above illustration, both x and y are variables this is since they may suppose different values throughout the analysis of the function. On another hand, a and b are referred to as constants since they suppose fixed values.
The variable y is a dependant variable in sense it means that the values of y are generated from an independent variable x.
The collection of every the values of the independent variable for that the function is defined is referred to as the domain of the function corresponding to this we have the range of the function that is the collection of all the values of the dependent variable defined with the function
The fact such is, it is a function of x can also be denoted via the given general form as
y = f(x)
Functions of a single (only one) independent variable may either be non linear or linear.
Represented Linear functions can be via:
y = a + bx
Whereas nonlinear functions can be represented via functions as like:
i. y = α_{0} + α^{3}_{1} x + α_{2}x^{3}
ii. y^{2} = 3x + 18
iii. y = 2x^{2} + 5x + 7
iv. ax^{2} + bx + cy + d = 0
v. xy = k
vi. y = a^{x}
Whereas: α, a, b, c, d, k = constants