00:01
In order to find an equation for the graph, we need to consider the general equation of a sign function, which is given here.
00:09
And we need to identify what each of these letters stand for.
00:12
So a is the amplitude of your graph.
00:17
B is the frequency, which is also found by doing 2 pi divided by whatever your period is.
00:28
C is the horizontal shift, and d is the vertical shift.
00:40
So if we can identify all of those things from our graph, we'll replace those into the letters there, and we will be good to go.
00:48
So if we look at our graph, we are tempted to find the amplitude first, but it's kind of hard to tell exactly where the middle of the graph is.
00:56
So let's first find the midline of our graph.
00:59
If you're looking at that graph, the top or a peak is at 7, and the bottom is at negative 1.
01:07
So halfway in between 7 and negative 1 would be 3, meaning that there is a midline right on the y value of 3.
01:18
And that would actually tell us the vertical shift.
01:21
That midline usually is at y value of 0.
01:25
But since it's at 3, we know that the vertical shift will be 3 for ours.
01:33
So we've already found d.
01:35
And now that we know that the midline is at 3, we can see that the amplitude will be the distance from 3 to 7, because that's where the top of the curve is, which is 4.
01:46
So we will be replacing a with 4.
01:49
That's the amplitude.
01:51
Now the frequency or the big letter b, we need to find the period first, and then we'll do 2 pi divided by that.
01:59
A period is the interval it takes to complete one full cycle...