Graph each function over a two-period interval. Give the perio...

Question

Graph each function over a two-period interval. Give the period and amplitude. See Examples 2–5.

y = -2 sin 2 πx

Accepted Answer

Draw the graph of the function given below consider only two periods and determine the period and amplitude where our function is Y equals negative four sin by X. We're also given a coordinate plane to graph our function on. Now to graft this, we first need the standard form of the sine X function. This is given by a sign BX where A is our amplitude. And our period is given by the function equation two pi divided by B. Now we notice in our equation A is negative four B. It's just pie our period then will be two pi divided by pi which is just two. We now have enough information to graph our function. Let's set up five points to use for our equation. This will separate our period into four parts. We know X zero is where we start at which let's say X equals zero first because we're not shifting. Now, for each one of these X values, we are going to add period divided by four to each of them. This will divide our period into four equal parts. When we simplify our fraction, two divided by four gives us one half. So for every X value, we will add one half, X one, for example, is zero plus one half, which gives us one half, X two. We will take our previous answer one half and add another one half to get one X three. We will take our one plus one half to get three halves. And finally X four, we will take three halves, add one half to get two. We now have our X values which we can use to find our Y values. By making table, we will take all of our X values and then we will plug each of these values into our equation. Let's say our first one, it's negative four S pi multiplied by zero, that's negative four S zero, which is just zero. We will do the same for our following points. Our next one, for example, would be negative four sine pi multiplied by one half to get night before sun, I divided by two. You know S pi divided by two based on the unit circle is one. This gives us negative four. We will plug all of those in and end up getting 040 for our remaining points. Now, we can plot these onto our graph. Our first one, we see 800, followed by one half, negative four, 10, three halves or N 20. Now, because we want two periods, we will repeat this with our next points since the sign function loops indefinitely our next one will be five halves negative four following the same pattern. 30, seven halves, four N 40. Finally, we can make a smooth curve between all of our points down and up, down, up again and back down. This gives us the graph of our function Y equals negative four sine pi X OK. I hope to help you solve the problem. Thank you for watching. Good that.

Graph each function over a two-period interval. Give the period and amplitude. See Examples 2–5.
y = -2 sin 2 πx

Key Concepts

Period of a Trigonometric Function

Amplitude of a Trigonometric Function

Graphing Sine Functions

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