Some table of values for functions will not have a slope, or a constant unit of change for the x or y values. You must look for other patterns. Sometimes, the x is being multiplied by a factor in order to get the resulting output value. Make sure to consider all types of patterns in order to determine the relationship between the x and y values in a function.
When you're working with functions, one thing you have to be careful of, is sometimes you have lines and sometimes you have other shapes. So, we want to be careful that if it's not a constant change in X, with a constant change in Y, we might not have a line.
Look at this table. My X numbers have a constant change, I'm adding one each time but look at the Y numbers; I'm adding one, then adding 3, then adding 5, it's kind of weird. Since I don't have a constant change,that means I don't really have a slope. So in order to do this problem, I'm going to have to use some other patterns technique.
One thing that's really important to recognize is these numbers here. Do you guys know what they're called? Anyone? That's right, they're called perfect squares. These numbers are called square numbers because 2 times 2 gives you 4, 3 times 3 gives you nine. My next number pair in this chart would be 4, 16. And the way I'm doing this is because in my head I know the function looks like f(x) equals xÂ². Each input number gets multiplied by itself, to get the output number.
So I just wanted to throw this problem out there to show you guys that's it's really important to look for patterns. And sometimes you're not always adding a constant number, sometimes you have something like this, where it's another kind of pattern that you should really want to be aware of and look for in the Math world, where you have perfect squares.
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