Graph the trigonometric function.y = frac12 cot left( x -...

Graph the trigonometric function.\ $y = frac{1}{2} cot left( x - frac{pi}{4} ight)$ \ Start by drawing two consecutive asymptotes. Between those asymptotes, plot three points: a point where the graph intersects the x-axis, a point to its left, and a point to its right. Finally, click on the graph-a-function button.

Transcript

00:02 Okay, so i want to graph the function y equals one -half cotangent x minus pi over 4.

00:08 So on the first graph, i want to go over how to graph the parent function first.

00:15 So let's graph y equals cotangent of x first.

00:20 So on my cotangent graph, so at co -tangent at 0, your cotangent is undefined at piver 2 at 0, at pi it's undefined at 270 it's zero and it's back to undefined the other thing that i want to do because this problem said also to graph where it intersects the x excess a point to the left and point to the right i'm going to graph all the tangents at 45 so tangent in the first quadrant at 45 is one tangent at 135 is negative one tangent at 225 is positive 1, tangent at 315 is negative 1.

01:05 So i'm going to graph all of those in between as well.

01:07 So this is what my parent for cotangent looks like.

01:11 I have an undefined at 0.

01:14 I have 0 at pi or 2, undefined at pi, 0, undefined at 2 pi.

01:25 So there's my, and it says by drawing two consecutive asymptotes, i'm going to draw in 3 just so that you see them.

01:31 And then i'm going to plot at pi or four, i'm going to go up one.

01:39 3 pi over four, i'm going to go down one.

01:42 At 5 pi over four, i'm going to go up one.

01:44 At 7 pi per four, i'm going to go down one.

01:46 So this is what your parent function would look like for 0 to 2 pi on cotangent of x.

01:54 So when i want to do y equals 1 half cotangent of x minus pi over 4, okay, let's talk about what everything does.

02:11 So this one -half, this is a vertical shrink...

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