Polynomial and Rational Functions

A function of the form

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.

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.

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.

4. Polynomial of Degree 3

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

5. Polynomial of Degree 4

6. Polynomial of Degree 5

7. Polynomial of Degree 6