Determine the amplitude and the period of the shown function.
Okay, so to solve this problem, what we actually have to do is we need to determine what the amplitude and what the period are. So looking at the amplitude to begin, we can actually have a look at this definition. So the amplitude is the height from the center line to a peak or trough of the function.
So if you want to use this to find the amplitude of our function, the first thing we need to look at is this, the center line. So what is the center line of our function? I’ve actually shown the center line here and marked it on the graph. And it’s actually gonna be the 𝑥-axis. And the reason we know that is because actually the amount of- the size of the function above and below that center line is the same.
And in this case, you can actually say that there’s three units above and three units below. So now we actually want to find the amplitude of this function. We can actually see that we want the height from the center line to the peak or trough of the function. But we’ve actually already mentioned that cause it said the center line we have three units above or three units below cause it goes up to 𝑦 is equal to three or 𝑦 is equal to negative three.
So therefore, we can say that the amplitude of this function is equal to three. Great! So stage one complete. Now we can move on to the period.
So first of all, we wanna see what is the period. Well, the period is actually the length of one complete cycle of the function. But what does this mean? What does one complete cycle of the function actually tell us? Well, one complete cycle of a function is actually how long it takes for the function to repeat.
So here we can say we go from a peek to the next peak. That would be one complete cycle. Or we can go from a trough to the next trough because we’ve gone in the trough then we’ve got up to the peak and back down to the trough. Again, that’s one complete cycle, or even just two points where it crosses the 𝑥-axis at the same points.
So we can see that these crossing them both on the downstroke. So that again would be one complete cycle. And we can actually see from our graph that, for each of the complete cycles that I’ve shown, there’s a distance of 10 squares. So therefore, we can say the period is 10 squares. But what each square worth?
Well, if we get back to the scale, we can see that each square is worth 0.2. So therefore, we can say that the period is gonna be equal to two. And that’s because if we multiply 10 by 0.2, we get two. So we’ve now determined the amplitude and the period of the shown function. And the amplitude is equal to three. And the period is equal to two.