How to Graph Monomials

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When graphing monomials, the process is very similar to graphing a polynomial. Graph monomials with help from an experienced mathematics professional in this free video clip.

Part of the Video Series: Trigonometry, Graphs, & Other Math Tips
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Video Transcript

Hello, my name is Walter Unglaub, and this is how to graph monomials. So a monomial is simply a polynomial in which you just have one term in the expression. So, for example, a general polynomial f of x will be some constant for example, plus b times x-squared plus c time x-cubed, so on and so forth, as an example. And if we want to examine a monomial, we would have to just look at one of these terms. So a monomial I can come up with three different examples. Let's consider f of x is equal to 2x, and another monomial g of x is equal to x-squared, and finally a third monomial h of x is equal to x-cubed. So, these are different examples of monomials, and you can plot them if you understand the relationship between the independent variable and the dependent variable. So, for example here, if this is my f of x, and this is x, I'm going to have my slope of two. So here is the graph of my linear monomial. I can do the same for g of x and h of x. Now my g of x is gonna be equal to x-squared. So I have my vertex at the origin, and because it's an even function, because of this even power, I'm going to have an axis of symmetry at x is equal to zero. And finally, my third example I have h of x is equal to x-cubed. Now that function is going to look something like this. As I increase the value of the coefficient in front of the monomial term, then I'm going to essentially be stretching the graph along the vertical direction. And as I alternate between terms of even and odd powers, I'm going to be either getting monomials that look like this for even numbered powers, or asymmetric monomial graphs, such as this one, if the power is odd for the monomial term. My name is Walter Unglaub, and this is how to graph monomials.


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