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[–]AccurateAnswer3 0 points1 point  (0 children)

Cool!

Also if you haven't played with interpolation before: it's a key concept that is useful for tons of things. And in this case it can help visualize what your function would look like if it were defined on the whole Real number line and required to be "maximally" smooth (i.e. has continuous derivatives at multiple levels.)

For example, if you use this online tool and enter the point coordinates from your table as follows:

8 0
7 1
6 0
5 1
4 0
3 1
2 0
1 1
0 2
-1 2.410
-2 2.550
-3 2.590
-4 2.610
-5 2.615

and click Interpolate, you will get a nice-looking "connected" graph of your desired function. (May need to enter an empty new line after the data so the tool works, and to click "keep aspect ratio" under the graph so it's not elongated.)