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Chapter 4: Problem 11

Graph two periods of the given tangent function. $$y=\tan (x-\pi)$$

Short Answer

Expert verified
The graph of the function \(y=\tan (x-\pi)\) features asymptotes at \( x = \pi \pm \frac{\pi}{2} + k\pi \), crosses the x-axis at \( x = (k+1)\pi \) and includes a curve between the asymptotes for two full periods.

Step by step solution

01

Identify the Period and Asymptotes

The period of the function \(y = \tan (x-\pi)\) is \( \pi \). Asymptotes will be at \( x - \pi = \pm \frac{\pi}{2} + k\pi \), in other words it is at \( x = \pi \pm \frac{\pi}{2} + k\pi \) for all integer \( k \)
02

Identify the Zeros

The zeros of the function are at \( x - \pi = k\pi \), or \( x = k\pi + \pi = (k+1)\pi \). This means the function crosses the x-axis at \( x = (k+1)\pi \).
03

Plot the function

Plot the function \(y=\tan (x-\pi)\) by drawing the appropriate curves between and approaching the asymptotes. Create markings at the zeros of the function. Remember to plot two full periods of the function.

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Most popular questions from this chapter

Use a graphing utility to graph two periods of the function. $$y=3 \sin (2 x+\pi)$$

Use a graphing utility to graph each function. Use a viewing rectangle that shows the graph for at least two periods. $$y=\tan 4 x$$

Assuming Earth to be a sphere of radius 4000 miles, how many miles north of the Equator is Miami, Florida, if it is \(26^{\circ}\) north from the Equator? Round your answer to the nearest mile.

Graph one period of each function. $$y=-|3 \sin \pi x|$$

will help you prepare for the material covered in the next section. a. Graph \(y=-3 \cos \frac{x}{2}\) for \(-\pi \leq x \leq 5 \pi\) b. Consider the reciprocal function of \(y=-3 \cos \frac{x}{2}\) namely, \(y=-3 \sec \frac{x}{2} .\) What does your graph from part (a) indicate about this reciprocal function for \(x=-\pi, \pi, 3 \pi,\) and \(5 \pi ?\)
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