Polynomial and Rational Functions

A function of the form

`f(x)`=`a_nx^n +a_(n-1)x^(n-1) + ...+a_1 x+a_0`

is called a polynomial function. Here n is a non-negative integer and `a_n , a_(n-1) ,... a_2, a_1, a_0` are constant coefficients.


In this section, we briefly discuss the graphs of the polynomial functions.


1. Polynomial of Degree 0


The graph of the polynomial function f(x) = 0 is the x-axis.Also the graph of a polynomial function f(x) = c is a horizontal line as shown below.


Polynomial function f(x) = c

Polynomial of Degree 0


2. Polynomial of Degree 1


The graph of a polynomial function of the form f(x) = mx + c is a straight line. The slope of this line is m, whereas c is the y-intercept of the line as shown in the figure below.


Polynomial of Degree 1

Polynomial of Degree 1



3. Polynomial of Degree 2


The graph of a quadratic polynomial function is a parabola. This type of function has a form ` f(x) = a_2x^2 + a_1x + a_0 ` . A graph of such a function is shown in the figure below.


Polynomial of Degree 2

Polynomial of Degree 2



4. Polynomial of Degree 3


Similarly the graphs of a few higher degree polynomial functions have been shown below.

Polynomial of Degree 3

Polynomial of Degree 3



5. Polynomial of Degree 4


Polynomial of Degree 4

Polynomial of Degree 4



6. Polynomial of Degree 5


Polynomial of Degree 4

Polynomial of Degree 5



7. Polynomial of Degree 6


Polynomial of Degree 5

Polynomial of Degree 6








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