00:01
So in this problem, we're given the graph of y equals f of x, and we want to sketch this new graph for y equals one half of f of x plus two.
00:07
So we have to think about what transformation is going to happen.
00:10
Well, the key thing here is what's happening on the inside.
00:13
We're taking f of x plus two.
00:15
So we have to think of, well, for what value of x would bring us back to the original, so almost think if we were to substituting negative 2 for x, negative 2 plus 2 would be 0.
00:24
So we would take on the same value as when x was 0 in our original function.
00:28
Well, because we plugged in negative 2, that means we're first going to shift all of these points left two units.
00:35
Now, on the outside, we have our function getting multiplied by one -half.
00:38
So once we move each of these points to the left two units, then we're going to multiply their y value by one -half.
00:45
So we're going to have multiply y by one -half.
00:48
So now we can do each of this for the following points.
00:50
So if i start with negative 4 -9 -3, i'm going to move that left 2, but then i'll take half of negative 3, which is negative 1 .5.
00:57
So i'll know that the ordered pair, negative 6, and negative 1 .5, will be on the graph of our new function...