## Wednesday, March 7, 2007

### BOB

Hi everyone! Our unit on Transformations is almost done. We are now getting ready for the 2nd test. This unit has been really interesting. We learned a lot of things on how to shift, stretch and/or compress a function graph. We learned about the Standard Form, f(x) = Af(Bx-C) + D. Its a bit similar to the standard form of Trig. Functions, but the values work in a different way.

A affects the graph by stretching (A > 0), or compressing (0< A < 1) its y coordinate.
B affects the graph by stretching (0< B <1), or compressing (0 < B) its x coordinate.
C affects the graph by shifting it to the left (0>C), or shifting it to the right (C>0). Watch for the sign of C because the standard form changes the sign of C.
D affects the graph by shifting it to the left (0>C), or shifting it to the right (C>0).

We also looked at the Reciprocal Functions. We learned that the root of the original function, f(x), is the vertical asymptote of the reciprocal function. The invariant points, -1 & 1, are both in the function and the reciprocal function since the reciprocal of 1 & -1 are themselves. We learned how to graph the reciprocal function by doing the "Smallering & Biggering" Game.

We looked at The Absolute Functions. The first step is to graph the original function. Then any part of the graph below the x-axis must be reflected along the positive side of the y-axis.

Finally, we looked at Trigonometric Modeling. We're not quite familiar with the material yet, that's why we are continuing with our discussion.

I hope everyone will do well on the next test. ^_^