00:01
So we have our original function, and i'm just going to say it graphs like this with a vertex at the point 3 -2, and it has an intersection up here at 10.
00:13
And so it does this parabola, graphs that parabola.
00:17
And in a, we want to look at y equals one -half times f of negative x plus 2.
00:27
And so the first thing we need to do is reflect over the y -axis.
00:32
So this negative reflect over y axis.
00:38
So this point will move over here to negative 3, 2.
00:47
And then it will shift 2 left because of this x plus 2.
00:53
So it will be over here at negative 5 2.
00:57
And then it needs to vertically compress or vertically shrink by a factor of and half so this will compress down to a one and where this used to be at 10 it's going to end up being at 5 no i'm sorry that's that's not true it's going to keep that that same shape but it's it's not going to have that same value there at 10 anymore but it's going to compress down and so the graph would keep the same shape except it's going to compress down so where this was uh let's let's see, one, two, three units away, one, two, three units away, it would be down at five.
01:54
And back this way.
01:56
We need to close one little thing there.
02:02
For part b, for part b, we have the y minus two is equal to negative f of two of x minus three.
02:18
So for this we have again quite a few transformations taking place and so the graph is going to so this will horizontally horizontally compress so there's going to be a factor of one half so it's going to shrink horizontally so it's going to be less narrow then it's going to shift three right and then this negative is going to reflect over the x -axis, and then it's going to shift up to.
03:11
So the original parabola, again, crossed here at 3 and 10, 3 -2.
03:23
So it is going to get horizontally compressed by a factor of one -half.
03:30
So this graph is going to end up shrinking over to here, and this point's not going to.
03:39
So it's going to end up being this parabola that's going to look like this...