So what I did here was interpret the original function y=|x| (shown facing upwards in black) in these few different changes you see here in various colors. I started off with a vertical translation (as you can see in red), which is y=|x| + 3. It is still the same function, but it only moved 3 spaces up on the y-axis. The next one was a horizontal translation (as shown in blue) as y=|x - 1|. This here is moved to the right one unit of the x-axis. In green, I performed both a horizontal and vertical translation which is y=|x-2| + 3 (right two units, up 3 units). The next one was a reflection shown in purple, y=-|x|. As you can see, the original function is just simply reflected, so it's facing downwards. The last transformation that I graphed was all of these put together -- a vertical translation, a horizontal translation, and a reflection. And so, this is y=-|x-1|-1.Back to School Night Extra Credit:

For Back to School Night I had to bring my brother (my parents were unavailable for the time being -- my brother is old enough to be my dad though! Haha) and so I told him to choose a function. He chose the cubic root function because he said it looked cool, so I helped him through it. He said he does not even remember doing these translations in his high school years, but that was about 15 years ago. Overall it was fun teaching him, because he understands most of the stuff that I told him.

For Back to School Night I had to bring my brother (my parents were unavailable for the time being -- my brother is old enough to be my dad though! Haha) and so I told him to choose a function. He chose the cubic root function because he said it looked cool, so I helped him through it. He said he does not even remember doing these translations in his high school years, but that was about 15 years ago. Overall it was fun teaching him, because he understands most of the stuff that I told him.

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