7-3: Indentifying Functions from Numerical Patterns

Alright, this lesson is essentially determining the type of function (and it's corresponding pattern) from a set of points (arranged by x and y). It's easiest to break the lesson down by function, so sit back and follow along.

Linear Functions: X and Y values are increased by the addition of a constant amount to each variable. As you can see, we must add 2 for each x value to get to the next, and 3 to each y value to get to the next. Therefore, we refer to this as the "Add-Add Pattern."

X-Y
1-4
3-7
5-10
7-13
9-14


Exponential Functions: A constant value is added to each X value, and a different constant value is multiplied with each Y value. As you can see, 2 is added to every X value and each Y value is multiplied by 9. This is therefore called the "Add-Multiply Pattern."

X-Y
1-15
3-135
5-1215
7-10935

Power Functions: These suck. Just going to throw that out there. Anyways, the majority of X values are multiplied by a constant, just as the majority of Y values are multiplied by a different constant. I say "majority," because certain points simply don't fit the pattern. Go figure. But yeah, as stated earlier, the majority of X values are multiplied by 2 and the majority of y values are multiplied by 8. We ignore the point (9, 3645), because it simply doesn't fit the pattern. This pattern is "Multiply-Multiply"

X-Y
3-135
6-1080
9-3645
12-8640


Quadratic Functions: These are probably the strangest of the bunch. The X values are evenly spaced and added by a constant amount (in this case, 2) and the differences of the Y values are also evenly spaced. Note the "differences" there. Each specific Y value is added by a different amount each time, but they all share a common factor (in this case, 24). So therefore, this is called the "Constant Second-Differences Pattern."

X-Y
1-15
3-5
5-19
7-57
9-119



Example Problem: Determine 1) the type of function and 2) specific pattern from the following information....

X-Y
5-250
10-750
15-2250
20-6750

Solution: Alright, here's what you do. Notice that the X variable is added by a constant value, 5. Now, check out the Y column. These values are multiplied by a constant value, 3. This table therefore reflects an exponential function and the Add-Multiply Pattern.


Okay, we're almost done here. If you want more help, check out this handy website: HERE!

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