describe how the graph of y=(2x+2)^2 can be obtained from the graph of y=x^x.

Question

anonymous · Answer

x^x?

anonymous · Answer

x^2 sorry

anonymous · Answer

Ok, whew, thought I'd have to pull out some real funky voodoo for this one...

anonymous · Answer

First, examine what is different between these two functions:
$$y=x^2$$$$y=(2x+2)^2$$

anonymous · Answer

they are both square functions, but one has more too it than that.

anonymous · Answer

Right, and in particular, the only change was what was being squared; there wasn't anything added or subtracted at the end.

anonymous · Answer

That means there is no vertical translation (no shift up or down).

anonymous · Answer

Inside those parentheses, there are two things happening to the x. It is being doubled, which means y is going to treat it as twice as big before squaring it, so y is going to get bigger, faster.

anonymous · Answer

2x then has a +2 applied to it, so that will cause a horizontal translation to the left (again, because y is treating negative values of x as if they were positive, so things are happening sooner.