This will not be the case with all the functions we will meet in this course. Of course, in this age of calculators and computers, that does not seem like as much of an advantage as it did a hundred years ago. However, there is another reason why polynomials are interesting for us which can be explained by an analogy. Animal breeders often breed a new animal from two different parent so that the offspring inherits some desirable features from its parents. When you saw the liger, you could see that some parts of it looked like a lion while other parts looked like a tiger.
Polynomials are somewhat like the liger.
When you look at a polynomial, you can still see traces of the power functions which went into its construction. Let's try to illustrate what we mean with an example. Below is the graph of one of our power functions . By moving the box around, we can create different polynomials by adding a quadratic term. In terms of our analogy, we're building a new animal by adding varying amounts of a tiger to a lion.