What are Polynomial Functions?

masterwu (59)in #steemiteducation • 7 years ago

In this post, we will have a visual look at polynomial functions. Basically, if an equation can be expressed as...

where x is any real number, and...

and the constants...

are known as the coefficients, then P(x) is what we call a Polynomial Function. Now, so long as...

...then the polynomial is considered to be of degree n. What does this mean? Well, let's say...

This is a 1st degree polynomial (n = 1). We also know this to be a linear function. An example of a linear function is graphed in Figure 1.

Figure 1. 1st Degree Polynomial.
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In the above example, the coefficients are a = 2 and b = 1.

Is a 2nd degree polynomial. This is of course, a quadratic function. An example of a quadratic function is shown in Figure 2.

Figure 2. 2nd Degree Polynomial.
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Is a 3rd degree polynomial, and is also known as a cubic function, an example of which is shown below in Figure 3.

Figure 3. 3rd Degree Polynomial.
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Figures 4 and 5 demonstrate 4th and 5th degree polynomial functions respectively.

Figure 4. 4th Degree Polynomial.
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Figure 5. 5th Degree Polynomial.
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Notice that the maximum number of turning points in a polynomial of degree n is n-1. For instance, as we can see in Figure 5, the number of turning points corresponding to the 5th degree polynomial is 4.

Polynomials are a very useful mathematical tool for modelling real-life phenomena from moving objects in space to economics. And we will explore some examples of these in future posts.

Here's a list of posts created so far on the topic of Functions: