00:01
So in this problem, we're being asked to select the correct graph for the given function.
00:04
Y equals 3 times 2 to the x plus 2.
00:07
Well, keep in mind what your basic function would be.
00:10
Your basic function would be y equals 2 to the x.
00:13
So think about what this exponential function would look like.
00:16
Remember, these functions have a horizontal lachyatote at the x -axis.
00:21
And now let's consider what its y -intercept would be.
00:24
So if i just make a couple of tick marks here.
00:27
So you find your y intercept by substituting 0.
00:30
For x.
00:31
So we have y equals 2 to the 0, and 2 to the 0 is 1.
00:35
So that tells us the ordered pair is 0 1.
00:38
So our general function looks like this.
00:42
Okay, so now we have to consider the transformations that are happening to our function.
00:46
Well, first off, the fact that we're adding 2 at the end means that our graph is going to go up to.
00:51
And this 3 at the beginning means that we're going to have a vertical stretch by a factor of 3.
00:56
So vertical stretch.
01:03
Stretch.
01:04
Let's spell that correctly by 3, meaning all of the values in your problem are getting multiplied by 3.
01:13
Okay, so now let's apply this to our problem...