What are Polynomial Functions?
![b17.png](https://steemitimages.com/640x0/https://steemitimages.com/DQmRwQTSjZakxh3Dq8JbR6UAL7SoynAYnrwtMnfqBkP3QtS/b17.png)
In this post, we will have a visual look at polynomial functions. Basically, if an equation can be expressed as...
![b1.png](https://steemitimages.com/DQmPBcD1F7SR9c1d7gv4NBLNPZyy8Kn4Qwvkbq59mcMgXJN/b1.png)
where x is any real number, and...
![b2.png](https://steemitimages.com/640x0/https://steemitimages.com/DQmTUEKAv7hyGCeCTjmxuewpjXWBT6zv4hAq6nRhDWL35wa/b2.png)
and the constants...
![b3.png](https://steemitimages.com/DQmZSL2F8aR2464oR1fVq18VKT9mticuZUtJszCMyxuivqq/b3.png)
are known as the coefficients, then P(x) is what we call a Polynomial Function. Now, so long as...
![b4.png](https://steemitimages.com/640x0/https://steemitimages.com/DQmbWFEYmxYz384e26txxCVkz1q8F3wiMwWJ8bmfqtb28ph/b4.png)
...then the polynomial is considered to be of degree n. What does this mean? Well, let's say...
![b5.png](https://steemitimages.com/DQmPeahFUDJ4imSSuppHFfijoCSSSf48wSkBDcsTxkDA5Pa/b5.png)
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.
![b9.png](https://steemitimages.com/640x0/https://steemitimages.com/DQmRthUNQKMiMRtQswWofuR4Wa7SwGMavnPqq4hni6RxQkW/b9.png)
Figure 1. 1st Degree Polynomial.
Created with: www.desmos.com/calculator
In the above example, the coefficients are a = 2 and b = 1.
![b6.png](https://steemitimages.com/DQmZrsdEi76iQM9uDJvT4f3GyJiPpys2JaANw76kqDMPnsL/b6.png)
Is a 2nd degree polynomial. This is of course, a quadratic function. An example of a quadratic function is shown in Figure 2.
![b10.png](https://steemitimages.com/640x0/https://steemitimages.com/DQmage7TKWVEA8CirYigVkEXuAVzK5Fh23tiz2WoUSFKSKP/b10.png)
Figure 2. 2nd Degree Polynomial.
Created with: www.desmos.com/calculator
![b7.png](https://steemitimages.com/DQmWGkEyMR9BPnbVGXo1A54fvfmRRYNua1o9qV2ZDnwRpjY/b7.png)
Is a 3rd degree polynomial, and is also known as a cubic function, an example of which is shown below in Figure 3.
![b12.png](https://steemitimages.com/640x0/https://steemitimages.com/DQmNwXvg376bwg8e4yzufBH8A8eysrjCzJB7QCEzygq8qMo/b12.png)
Figure 3. 3rd Degree Polynomial.
Created with: www.desmos.com/calculator
Figures 4 and 5 demonstrate 4th and 5th degree polynomial functions respectively.
![b14.png](https://steemitimages.com/DQmU7New9qF2aWLG8WSLAo5fPFjv6qykVXnCg1MBEFDUZqS/b14.png)
Figure 4. 4th Degree Polynomial.
Created with: www.desmos.com/calculator
![b16.png](https://steemitimages.com/640x0/https://steemitimages.com/DQmVfQmrZdSB3LiVFL7RPQdZCtjLB1DCnKVjPLmuFtSzhsF/b16.png)
Figure 5. 5th Degree Polynomial.
Created with: www.desmos.com/calculator
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:
- Drawing piecewise defined functions
- What are Polynomial Functions?
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