<p>That’s great drexter. As some of you (including myself) have pointed out, there is nothing in this thread that is absolutely necessary to get an 800. Nonetheless, I expect that many of you will find the strategies that we discuss here useful. Pick out the ones that you find most helpful. </p>
<p>Just one comment on the basic transformations: Note that the vertical transformations behave as you would expect, and the horizontal transformations behave opposite from how you would expect. For example replacing x by x-3 shifts the graph to the right 3. </p>
<p>I will post additional solutions to the rate problem shortly and then I’ll get back to counting problems. After that I’ve got a lot more good stuff to come…</p>