How do you graph, identify the domain, range, and asymptotes for $y = tan (2 x + \frac{π}{2})$ $y=tan(2x+pi/2)$ ?

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How do you graph, identify the domain, range, and asymptotes for $y = tan (2 x + \frac{π}{2})$ $y=tan(2x+pi/2)$ ?

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Answer 1 · 2018-07-25T02:44:05

Domain: $x \neq \frac{k}{2} π, k = 0, \pm 1, \pm 2, \pm 3, . .$ $x ne k/2pi, k = 0, +- 1, +- 2, +- 3, ..$
Range: $(- \infty, \infty)$ $( - oo, oo )$ .
Asymptotes: $x = \frac{k}{2} π, k = 0, \pm 1, \pm 2, \pm 3, . .$ $x = k/2pi, k = 0, +- 1, +- 2, +- 3, ..$ . See grapj.

Explanation:

$y = tan (2 x + \frac{π}{2}) = - cot 2 x,$ $y = tan ( 2x + pi/2 ) = - cot 2x,$

$x ne 0, +- pi/2, +- pi, +- 3/2 pi, +-2pi, ...$

Graph of $y = tan ( 2x + pi/2 )$ :
graph{y-tan(2x+pi/2)=0}

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How do you graph, identify the domain, range, and asymptotes for $y = tan (2 x + \frac{π}{2})$ $y=tan(2x+pi/2)$ ?

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Explanation:

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How do you graph, identify the domain, range, and asymptotes for $y = tan (2 x + \frac{π}{2})$ $y=tan(2x+pi/2)$ ?