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 = π sin πx

Accepted Answer

Draw the graph of function given below consider only two periods and determine the period in amplitude where our function is Y equals three pi sine four pi X and were given a coordinate plane to graph or function on to solve this. We'll first look at the general form of sin X. This is given by the equation Y equals a sine BX. Now, our amplitude S equals to a arion equals to two pie divided by B. Now if you look at our function, our amplitude A is three pi and our period is two pi divided by four pi which is just one half. Now, we can find X values for our function. Let's say we start at X zero is equals to zero. This is because we aren't shifted to the left or to the right. So starting at zero, we'll find or more points to do this. Let's divide our period by four period divided by four, gives us one half divided by four which is 1/8. We can now add 1/8 to every one of our points starting at zero X one, then will be zero plus 18 which is just 18 X two will be our previous answer. 1/8 plus our period divided by 4, 1/8. This gives us 1/4 X three will be 1/4 plus 1/8 which gives us re eights. It takes four B 3/8 plus 1/8 to give us four eights, which is also one half. We don't have five X values to use and we can now find some Y values from those X values. We can make a table with all of our values. Now, let's plug in some values. We have three pie sign four PX. Literally plug in our first one being repay sign four pi multiplied by zero, which gives us three pi sign zero, which is just zero. We can do the same for all of our following points. Our next one, we get three pie sine or pi multiplied by 1/8 to get three pie. So hi divided by two which just gives us three pack. If we continue, we would get zero negative three pi and zero again. Now we can graph all of these on our plane here. Our first point being 00. Our next point being 1/8 3 pie just way up around there, 140, 3/8 negative three pi down there somewhere and one half zero. Since we want two periods, we will repeat this and loop them again. I'll adjust this point just a little bit over to the right. We will once again, go up 23 P down to zero down again. 235 in night. The three pie should sing and back up to zero when we get to one now, just draw a smooth curve between all of our points giving us our function. Repay sign or PX. Ok. I hope to help you solve the problem. Thank you for watching. Goodbye.

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

Key Concepts

Period of a Trigonometric Function

Amplitude of a Trigonometric Function

Graphing Trigonometric Functions

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