00:01
In this problem, we're told that the point 3, 0 .8 is on the graph of the function, y equals f of x.
00:08
If this function is transformed in turn to the function y equals 4 times f of 2x plus 2 minus 6, then our job is to find the new transformed point.
00:22
So let's take our point 3 ,000 8 on the graph of y equals f of x.
00:27
And let's note that this gives us a very important relationship between the x and y coordinates, we know that f of 3 equals 8.
00:38
That is equivalent to saying that the point 3 comma 8 is on the graph of y equals f of x.
00:45
So we want to use this relationship, and we want to come back and find the new transformed point one step at a time.
00:54
So let's copy the transformation function over again.
00:59
We've gone from y equals f of x.
01:05
To y equals 4 times f of 2x plus 2 minus 6.
01:14
And we're going to start here with the input.
01:18
One way to do this is to say we want that input to match the input we have, namely the 3.
01:25
So if we set 2x plus 2 equal to 3, then we can solve for x and find the x coordinate of the new transformed point.
01:36
So this tells us that 2x is 1, and therefore the x coordinate we want is 1 half.
01:46
So here's one way to find the x coordinate of the new transformed point.
01:51
Now another way is to take the 2x plus 2 in parentheses there and say since we're adding 2, we have to take our 3 we started with and subtract 2.
02:01
We have to move left 2, so 3 minus 2 is 1.
02:04
And then since we're doubling the input, we have to divide that by 2...