So, our second unit is coming to a close and now another gruesome test approaches our cowering souls. But despite the oncoming test, I feel as though this unit wasn't even a full unit, but yet we learned quite a bit in this unit, the unit of Transformations. That might be due to the fact that I have always found graphing to be very simple and straight forward, and this unit didn't present any exception to this. Some review questions did require deep contemplation, although these questions weren't particularly concerning graphing so there isn't much worry there. I hope everyone else, as I successfully accomplished, finished all of the homework that was given to us. It's very important, and in graphing I really think it's helps with our conceptual understanding as we become more habitual to graphing each type of function transformation. But overall, the unit of Transformations didn'y present any particular tribulations to me, and was a really easy unit. Only thing I didn't like was the quiz. Why do I never take time to read the questions? Now I'll know, good timing as well, as our pretest is tomorrow, and I'll try not to fall victim to one of Mr. K's tricks. But now we know all about that now, since we are past our first marker of the year, the end of our first unit.
But our second unit not only marked the triumph over our first obstacle, the circular functions test, but it was also a marker for another triumphant feat. This feat of course is the utilization of our smartboard throughout the unit of Transformations. Since the time we first received the smartboard, Mr. K has been practicing his smartboarding skills and now it's more than just incorporated into our daily lessons, but is the basis of where we conduct all of our lessons. We now all come up to share our answers with the class on the smartboard, and I think it's ingenious the way Mr. K set up this peer evaluation process mixed with some competitive vigor to help our overall education. With the smartboard, now we're all willing to go up and put up our answer, and whether we're correct or incorrect, we inevitably end up learning. I wonder what the year would have been like without the almighty smartboard.
- Inverse functions are different from recipricol functions. f-1(x) is not f to the exponent -1, it's an inverse where you switch y and x coordinates, or flip it over both the y and x-axis'. Simple.
- Always stretch the graph before translating it.
- To graph reciprocal functions, first find the invariant points. These are points where both graphs go through, and these points are always -1 and 1. Then find the root(s), these are where the vertical asymptote(s) will be for the reciprocal. Then, draw the reciprocal by drawing it increasing in value positively when the function is decreasing positively, the same for the negative direction (or vice versa if drawing the original function).
- Even functions are different from odd functions. Even functions are symmetrical over the y-axis, while odd functions are symmetrical over the origin, meaning odd functions are the same if you turn the graph 180 degrees.
- Watch for the sign of a when considering translations in the general form: y = f(x-a)+b
And that's my BOB folks, again, sorry it's long, but I tend to ramble on... (=
GOOD LUCK TO EVERYONE ON TOMORROW'S PRETEST, AS WELL AS OUR TEST ON WEDNESDAY. (Dates may not be exact, as Mr. K said)