Function Family Guy

I discussed my approach to function families in an earlier post. The instructions for each of these graphing activities were the same:

Write an equation for each of the following exactly as you would enter them into your Nspire, sketching the graph of each as you go. Only when you have checked your equations and graph with me should you graph them on the Nspire.

Nothing fancy, but it was fun. Kids whined about the numbers (too many decimals), and argued about the finished result (there are two famous football-shaped headed cartoon characters). We did all of these on the Nspire (hmm...might be my first Nspire-related post), but we also used GeoGebra. There are some differences in how you enter the equations which make the Nspire a little better for this activity.

For example, to enter the equation of a parabola from vertex A to B in the graph below, it would look like this on the Nspire

But like this in GeoGebra

I think this might be one area where the Nspire is superior, but even as I write this sentence, I think of how graphing circles and and other equations is so much easier in GeoGebra. You do not need to isolate y in order to graph a function in GeoGebra. You can graph non-functions like x = 4. Ellipses and Hyperbolas are peices of cake (or of cones...you choose).

For example, graphing circles in GeoGebra look like this

 but look like this in the Nspire

where you must graph the circle in two parts, top and bottom. Of course, I hope that by now, my students will graph a circle on the Nspire like this,

using function notation and the algebraic representation of geometric transformations, reflecting the top half of the circle in f1 over the x-axis, then translating the reflected circle up six units.

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1. A parabola with vertex A, from A to B.
2. A parabola with vertex A, from A to C.
3. A parabola with vertex D, from D to F.
4. A CUBIC with inflection point D, from D to E.
5. The LEFT HALF of a circle from B to E.
6. The RIGHT HALF of a circle from C to F.
7. A line segment from (1,1) to (1.5, 0.5).
8. A line segment from (1.5, 0.5) to (1,0).
9. The LEFT HALF of a circle, centered at (1,-1) and radius of 0.5.
10. A circle centered at (-3,1) with a radius of 1.25.
11. A circle centered at (4, 0.5) with a radius of 1.25.
12. A parabola from the vertex (3,2) and stopping at (4, 2.25).
13. A parabola from the vertex (-2, 2.5) and stopping at (-3, 2.75).
14. A parabola with vertex (4,0), opening downward, from (3, -0.25) to (5, -0.25).
15. A parabola with vertex (-3,0.5), opening downward, from (-4, 0.25) to (-2, 0.25).

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1. Circle centered at (1,3) with radius 0.5.
2. Square root from vertex (1.5, 3) to (0.5, 3.25).
3. Square root from vertex (0.5, 3) to (-0.5, 3.25).
4. Square root from vertex (0.5, 3) to (-2, 2.75).
5. A cubic from inflection point (-2, 2.75) to (-3,2).
6. A parabola with vertex (1, 3.75) from (0, 3.5) to (2, 3.5).
7. A circle with center (-3,1) and radius 1.
8. A cubic from inflection point (-2, -0.75) to (-3,0).
9. A square root from vertex (0.25, -1) to (-2, -0.75).
10. A parabola from vertex (0,-1.25) to (-1, -0.75).
11. A parabola with vertex (2.25, 3.75) from (1, 3.5) to (3, 2).
12. The bottom half of a circle centered at (2.25, 2) with radius 0.75.
13. A parabola with vertex (-0.25, 3.75) from (-1, 2.75) to (0, 3.5).
14. A square root from vertex (2.75, -1) to (2.5, 1.25).
15. A parabola with vertex (1, -1.5) from (-1,-1) to (3, -1).