Find the period and sketch the graph of the equation. Show the asymptotes. y=tan(π)/(3) x

Name: Problem 14, Chapter 5: Precalculus: Functions and Graphs
Uploaded: 2021-06-16T00:49:20-08:00
Duration: 3 min 41 s
Channel: Eric Mockensturm
Description: Find the period and sketch the graph of the equation. Show the asymptotes. y=tan(π)/(3) x

step 1 We're asked to take a look at this function. Y equals tangent of pi x over 3. Find the acutes an

Find the period and sketch the graph of the equation. Show...

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Vertical Asymptotes

Vertical asymptotes are lines which the graph of the tangent function approaches but never touches, occurring when the function's argument is equal to ?/2 plus any integer multiple of ?. Identifying these asymptotes is essential because they indicate points of discontinuity in the graph where the function's value becomes unbounded.

Graph Transformations of Trigonometric Functions

Graphing the equation involves applying horizontal scaling transformations to the basic tangent function. This includes adjusting the period as well as marking the locations of the vertical asymptotes. Understanding these transformations helps in sketching an accurate graph and analyzing the behavior of the function over its domain.

Tangent Function Period

The period of a tangent function is the distance over which the function completes one full cycle before repeating. For a function in the form y = tan(Bx), the period is given by ?/|B|. This concept is crucial for understanding how horizontal scaling affects the frequency with which the pattern repeats along the x-axis.

Transcript

00:01 We're asked to take a look at this function.

00:03 Y equals tangent of pi x over 3.

00:07 Find the acutes and find the period.

00:11 So the period is going to be pi times the period over 3 equals the normal period for a tangent is pi.

00:23 So the period in this case is going to be 3.

00:26 And you can see here that i've actually plotted over from minus 3 to 3, which means that it is i plotted two periods of this function.

00:38 So i have a half period, a full period, and then another half.

00:43 Now to find the asymptotes, we need to set the argument of the tangent function equal to n pi minus pi over two.

00:55 That's when this is when the cosine function is zero for all integer value.

01:02 Of n cosine is 0.

01:05 So that means the tangent is going to be infinite, which means we have an acetope.

01:10 And we can see here that, let's see here, our pies cancel out.

01:16 And we get that x equals 3n minus 3 halves.

01:26 That is where our acototes are.

01:28 So when n equals 0, we have 1 at minus 3 halves, or minus 1 1 1 .5, which is right here.

01:35 When n equals 1, we have, let's see here, we have 1.

01:38 This would be 3 minus 3 halves, is positive, is 3 halves.

01:43 And so that's another 1 1 .5 right here...

Please give Ace some feedback