Using a Table to Graph Functions

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When using a table to graph functions, don't pick only positive or negative numbers in order to get a good range. Find out how to graph Y = X cubed with help from a math teacher in this free video on math functions and lessons.

Part of the Video Series: Math Functions & Techniques
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Video Transcript

So, how do you use a table to graph functions? Hi. I'm Jimmy Chang. I've been teaching college math for nine years. And we all know how to graph, but how do you use a table to help graph a function? That can seem kind of intimidating. Well, believe it or not, using a table is actually pretty straight forward. There's just a couple of things you want to think about. So, here's an example. Suppose you wanted to graph Y = X cubed. Now, generally you want to choose a series of numbers for X, and then the Y coordinates will fall out pretty quickly. But, a tip though is, you always want to be sure to pick out an evenly spaced out X coordinates. In other words, you don't want to pick strictly positive numbers and you don't want to pick strictly negative numbers. You kind of want to spread yourself out a little bit. So, a good range, typically, is negative 2 to 2. They're not too large, but they're pretty easy to plug in and it gives you an idea, typically, as to what a graph might look like. So, here we go. Let's just say you're plugging in 2, 1, 0, 1 and 2. Once you have your X coordinates, plug them in, and you'll figure out what your Y coordinates are fairly quickly. Now, the function here is Y = X cubed. So, first of all, we're going to plug in 2 in place of X. So, the first Y coordinate is going to be whatever 2 cubed is. Well, 2 cubed is going to give you 8. So, when X = 2, they Y coordinate is 8. When X = 1, you're going to have 1 cubed, which will then equal to 1. So, when X = 1, Y = 1. Sometimes the X and Y coordinates match. Now, when X is zero, you have zero cubed and you know zero cubed is going to give you zero. Now, supposing, since you already picked 1 and 2, how about (-1) and (-2)? Now, (-1) cubed --it's always good to write the negative number in parenthesis, whenever you can -- (-1) to the third power is going to give you (-1). So, when X = (-1), Y= (-1). Again, they match, but sometimes that happens. And then, when X = (-2), (-2) to the third power is going to give you (-8). And that's going to give you an idea as to what the X cubed graph is going to look like. All you have to do next is make a grid X/Y axis, plot these five points and then just extend the graph and you'll see what the graph looks like. So, I'm Jimmy Chang and that is how you use a table to graph functions.

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