We have a periodic

function depicted here and what I want

you to do is think about what the midline

of this function is. The midline is a line,

a horizontal line, where half of the

function is above it, and half of the

function is below it. And then I want you to

think about the amplitude. How far does this function

vary from that midline– either how far above does it go or

how far does it go below it? It should be the same amount

because the midline should be between the highest

and the lowest points. And then finally,

think about what the period of this function is. How much do you have

to have a change in x to get to the same

point in the cycle of this periodic function? So I encourage you to pause

the video now and think about those questions. So let’s tackle

the midline first. So one way to think

about is, well, how high does this function go? Well, the highest y-value for

this function we see is 4. It keeps hitting 4 on

a fairly regular basis. And we’ll talk about

how regular that is when we talk

about the period. And what’s the lowest value

that this function gets to? Well, it gets to y

equals negative 2. So what’s halfway

between 4 and negative 2? Well, you could eyeball

it, or you could count, or you could,

literally, just take the average between

4 and negative 2. So 4– so the midline is going

to be the horizontal line– y is equal to 4 plus

negative 2 over 2. Just literally the

mean, the arithmetic mean, between 4 and negative 2. The average of 4 and

negative 2, which is just going to

be equal to one. So the line y equals

1 is the midline. So that’s the midline

right over here. And you see that it’s kind

of cutting the function where you have half of the

function is above it, and half of the

function is below it. So that’s the midline. Now, let’s think

about the amplitude. Well, the amplitude is

how much this function varies from the midline–

either above the midline or below the midline. And the midline

is in the middle, so it’s going to be the

same amount whether you go above or below. One way to say it is, well,

at this maximum point, right over here, how far above

the midline is this? Well, to get from 1

to 4 you have to go– you’re 3 above the midline. Another way of thinking

about this maximum point is y equals 4 minus y equals 1. Well, your y can go as much

as 3 above the midline. Or you could say your

y-value could be as much as 3 below the midline. That’s this point right over

here, 1 minus 3 is negative 1. So your amplitude right

over here is equal to 3. You could vary as much as

3, either above the midline or below the midline. Finally, the period. And when I think

about the period I try to look for a relatively

convenient spot on the curve. And I’m calling this

a convenient spot because it’s a nice– when

x is at negative 2, y is it one– it’s at a

nice integer value. And so what I want to do is

keep traveling along this curve until I get to the same y-value

but not just the same y-value but I get the same

y-value that I’m also traveling in the same direction. So for example, let’s

travel along this curve. So essentially our

x is increasing. Our x keeps increasing. Now you might say, hey, have

I completed a cycle here because, once again,

y is equal to 1? You haven’t completed a cycle

here because notice over here where our y is increasing

as x increases. Well here our y is

decreasing as x increases. Our slope is positive here. Our slope is negative here. So this isn’t the same

point on the cycle. We need to get to the point

where y once again equals 1. Or we could say, especially in

this case, we’re at the midline again, but our

slope is increasing. So let’s just keep going. So that gets us to

right over there. So notice, now we have

completed one cycle. So the change in x needed

to complete one cycle. That is your period. So to go from negative 2

to 0, your period is 2. So your period here is 2. And you could do it again. So we’re at that point. Let’s see, we want to

get back to a point where we’re at the

midline– and I just happen to start right

over here at the midline. I could have started

really at any point. You want to get

to the same point but also where the

slope is the same. We’re at the same point

in the cycle once again. So I could go– so if I travel

1 I’m at the midline again but I’m now going down. So I have to go further. Now I am back at that

same point in the cycle. I’m at y equals 1 and

the slope is positive. And notice, I traveled. My change in x was the

length of the period. It was 2.

Is the equation 3sin(x)+1?

Those of you who are watching this from Flint Hill! Do this for Sal!!!!

https://www.khanacademy.org/math/trigonometry/trig-function-graphs/constructing-sinusoids/v/trig-function-equation

Important for completing the problem.

makes more sense than my teacher lol

Can you please create subtitle in Bengali for every videos?

How do you know if you need to add or subtract? Confused

Simple and short nice

How would you find the midline if you didn’t have a picture?

what about vertical shift?

Where is the the arabic caption