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Graphing Functions of the form x n

A polynomial function is a function in which f ( x ) is a polynomial in x .

A polynomial function of degree n is written as f ( x ) = a n x n + a n 1 x n 1 + a n 2 x n 2 + ... + a 2 x 2 + a 1 x + a 0 .

The graph of a polynomial function of degree 0 , which is of the form f ( x ) = a is a horizontal line .

The graph of a polynomial function of degree 1 , which is of the form f ( x ) = a x + b , a 0 , is a non-horizontal line. Read more about graphing lines here .

The graph of a polynomial function of degree 2 , also called a quadratic equation , which is of the form f ( x ) = a x 2 + b x + c , a 0 , is a parabola. Read more about graphing parabolas here .

Higher-degree polynomials can be somewhat more difficult to graph. Some easy cases are the parent graphs f ( x ) = x 3 , f ( x ) = x 4 , f ( x ) = x 5 , etc. These graphs have a predictable shape depending on whether the exponent is even or odd, as shown below.

Other higher-degree polynomials with more terms require other techniques. One method is to factor the polynomials to find x -intercepts.

You can also use calculus to find the critical points of a polynomial function.