Types of Function based on Equation

Types of Function based on Equation

Algebraic expressions are also included in the types of functions and are based on the degree of the polynomial expression.

 For example:

* The polynomial function with degree zero is declared to be a constant function.

* The polynomial function of degree one is termed a linear function.

* The polynomial function of degree two is termed a quadratic function.

* Similarly, the polynomial function of degree three is a cubic function.

Identity Function

The identity function is the kind of function that provides an identical input as the output. It is represented as, f(x) = x, where x ∈ R.

 For example, f(5) = 5 denotes an identity function. This implies that the identity function possesses an identical domain and range. The domain and range of the identity function are of the pattern {(1, 1), (2, 2), (3, 3), (4, 4)…..(n, n)}.

                               

The graph of the identity function is a straight continuous line that is fairly inclined to the coordinate axes and is crossing through the origin. The identity function can practice both positive and negative values and therefore it is present in the first and the third quadrants of the coordinate axis as can be seen from the above graph.

 Linear Function

A polynomial function with the first-degree equation is said to be a linear function. The domain and range for such a function is a real number, and it produces a straight-line graph.

 Equations such as y = x +5, y = 2x, y = 4x – 1, are all examples of linear functions. The identity function of y = x can also be included in the linear function.

Check out the graph for y = x – 6.

The general form of a linear function is f(x) = px + q, where p, q are real numbers. Graphically the linear function can be interpreted by the equation of a line y = mx + c, where m denotes the slope of the line and c implies the y-intercept of the line.

 Quadratic Function

A Quadratic function is a kind of function that holds the highest power two in the polynomial function.

For example,  is a quadratic function. The graph of a quadratic equation follows a non-linear pattern and is shape of parabola as can be seen from the below graph.

                                      

 In other words, a quadratic function is one with a second-degree quadratic equation and it has a graph that forms a curve. The general pattern of the quadratic function is where a ≠ 0 and a, b, c are constant with x as the variable. The domain and range of the quadratic function is R.

Cubic Function

A cubic function as the name implies is a sort of function that has the highest power three in the polynomial function.

For example, f(x)=x3 +9 is a cubic function.

The general form of a cubic function is where a ≠ 0 and a, b, c, and d denote the real numbers and x is a variable.

The graph of a cubic function is more curved than the quadratic function. The domain and the range are R. Check out the graph for        
                  
                                                  

Polynomial Function

A Polynomial function is a sort of function that can be represented as a polynomial. It is expressed as,

 where n represents a non-negative integer and

For Example f(x)=4x+12 is a polynomial function.