Graph each function over a one-period interval. See Examples 1...

Question

Graph each function over a one-period interval. See Examples 1–3.

y = tan 4x

Accepted Answer

Graph. The following function considering only one period Y equals 10 to X. Now we're also given a cord in the plane to grab our function on which we can see right here answer this. We need to look at some attributes of tangent X. So normally in a tangent function, our asymptotes occur at negative pi divided by two and pi divided by two. Now we have T two X which means we will replace our X with two X. Now we just want to solve for X to find our new ascents by dividing everything by two, we get negative pi divided by four and positive pi divided by four in our Essy to occur those two values. Now, in a tangent graph, we just need to find three points. Now we can find the midpoint between our two ascent toes by adding our two asymptotes together and dividing by two, which we will note this as the midpoint. We get negative pi divided by four plus pi divided by four, which gives us zero, divided by two, which is just zero. Now, since this tangent isn't shifted upwards, our midpoint occurs at 00, we now need to find two more points, we can find the midpoint between our X intercept or 00 and our Asymptote. So for two other points, let's say we take our left Asymptote negative pi divided by four, it added to Rx intercept X value zero, dividing by two. This gives us negative pi divided by four all divided by two, which is negative pi divided by eight. We can do the same for our positive Asymptote. I divided by four plus zero, divided by two gives us pi divided by eight. Now in a tangent function, if we don't shift our corresponding Y values will be Y equals one, Y equals negative one which means or negative pi divided by eight are point has Y equals negative one and four pie divided by eight. Our point has Y equals positive one. As long as you don't shift the tangent graph no should be a negative one and one for our wives. We now have three points and two asymptotes to plot on our graph are asym toes be said before or positive pi divided by four and negative pi divided by four. And our points we have 00 pi divided by eight positive one, negative pi divided by eight negative one. We now destroy a smooth curve between our points to give us our graph of why equals 10 to X. OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

Graph each function over a one-period interval. See Examples 1–3.
y = tan 4x

Key Concepts

Period of Trigonometric Functions

Graphing the Tangent Function

Transformations of Functions

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