SOLUTION: Sketch two periods of the graph for the following function. j(x)=tan(pi/4x) Identify the stretching factor and period. Identify the asymptotes in the displayed domain of the gra

Algebra ->  Trigonometry-basics -> SOLUTION: Sketch two periods of the graph for the following function. j(x)=tan(pi/4x) Identify the stretching factor and period. Identify the asymptotes in the displayed domain of the gra      Log On


   

Question 1203774: Sketch two periods of the graph for the following function.
j(x)=tan(pi/4x)
Identify the stretching factor and period.
Identify the asymptotes in the displayed domain of the graph you selected above. (Enter your answers as a comma-separated list of equations.)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

+j%28x%29=tan%28pi%2F4x%29

use the form +j%28x%29=a%2Atan%28bx-c%29%2Bd+to find the amplitude, period, phase shift, and vertical shift
in your case, a general equation is +y=A%2Atan%28Bx%29
We can identify horizontal and vertical stretches and compressions using values of +A and ++B. The horizontal stretch can typically be determined from the period of the graph. With tangent graphs, it is often necessary to determine a vertical stretch using a point on the graph.
Because there are +no maximum or minimum values of a tangent function, the term amplitude cannot be interpreted as it is for the sine and cosine functions. Instead, we will use the phrase +stretching%2Fcompressing factor when referring to the constant ++A.
The stretching factor is +abs%28A%29

The period is ++P=pi%2Fabs%28B%29
.
The asymptotes occur at +x=pi%2F2abs%28B%29%2B%28pi%2Fabs%28B%29%29k where +k is an integer.
stretching/compressing factor: +none
period: +P=pi%2Fabs%28pi%2F4%29=4
phase shift: +none
vertical shift: +none
horizontal asymptotes:++none
vertical asymptotes: +2%2B4k
in two periods, you have asymptotes:
+x=2
+x=-2
oblique asymptotes: +none

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