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The graph of a periodic function f is shown below

f(0)

3

What is the period of f?

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b What is the midline for f?

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What is the amplitude of f?

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Write a function formula for f. (Enter “theta” for 0.)

f(0)

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05:12

a. Open-Ended Draw a periodic function. Find its amplitude and period. Then sketch a translation of your function 3 units down and 4 units to the left.b. Critical Thinking Suppose your original function is $f(x) .$ Describe your translation using the form $g(x)=f(x-h)+k .$

00:38

For the graphs below, determine the amplitude, midline, and period, then find a formula for the function.

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04:01

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Transcript

So in this problem you were given the graph of a periodic function and part A. You were asked to find the period, Remember the period how long it takes to get from one point back to the starting point, which you found to be two units, which is perfect. Then the midline, you almost want to think about it as being your halfway point. So as you correctly identified it, it would occur at negative one. Now the next thing you want to do is you want to find the amplitude. Now the amplitude represents the height of the curve amplitude. Let’s go ahead and actually spell that correctly. So amplitude. There we go. Alright, so to find the amplitude, we can do this in a couple of different ways. First it’s really just the height of your curve. So if you take your midline which occurs when y is equal to negative one and the height, the max value occurs at one. So the distance between with equal to two. So that would represent your amplitude. Now the last thing you want to do is you want to write an equation. Now in this particular case, I’m going to do it in terms of cosine. And the reason why I do that is because our Cosine graph starts at the max decreases and increases So to write our equation f of theta, it’s…

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