Long lesson.
I began the lesson by talking about parent functions. So I put y = |x| on the board and put its graph up on the overhead screen using Sketchpad.
I then asked the students how they would think I would have to change y = |x| so the the graph would move up three units. They didn’t have any idea. I asked them, “would the x-part or the y-part change if you were moving a graph up?” They knew that it would be the y. So I then asked, “Would you change the y to a “y + 3” or to a “y – 3″? This is a leading question, of course, but I thought that it would be much quicker than making a t-table and making a rule plus the same question will be asked so many times over the course of the day that they might get used to asking themselves the question.
The students all said that “y + 3″ would be appropriate. So I told the students to read the parent function back to me but to replace the y with a y+3. I then told them that I could not type in a function into the computer unless it was solved for y, so we got y = |x| – 3. I then graphed it and we saw that we didn’t get the new graph (graphed in red) to move up, but down. So we changed the original y + 3 to a y - 3 and re-graphed the problem, and this time it was correct.
From then on I did lots and lots of examples with the absolute value function….trying to get the students to understand that if I wanted to translate one way, then their substitution of the form “x + h” or “y + k” would be counterintuitive – left means +h, right means -h, and so on.
After those, I began doing the problems again with y = x² making sure that the students understand that it doesn’t matter what parent function we are using, the rules are the same for translations.
Once those were done, I did one example with an exponential.
Then I put the problems on the PowerPoint on the board – graphs of absolute value, parabolas, and exponentials that have been translated and we came up with the equations. For these, I would ask the students to tell me what the parent function was. I’d write that on the board. Then I would ask how the function has been translated in words and write that on the board. Next I’d ask for what needs to be substituted such as changing x to a x + 3. Then I would physically erase the x in the equation and replace it with an x + 3 to show that step. Once we had the final equation, I’d put a rectangle around it and say that it was the equation for the graph on the screen.
For homework, I gave the Practice Your Skills worksheet for the section.
