Question #342c3

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Question #342c3

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Answer 1 · 2017-08-21T12:45:17

Please see below.

Explanation:

$y = 2 tan (4 x - 20) = \frac{2 sin (4 x - 20)}{cos (4 x - 20)}$ $y = 2tan(4x-20) = (2sin(4x-20))/cos(4x-20)$

has no horizontal asymptottes. (There is no limit as $x \to \pm \infty$ $xrarr+-oo$ .),
and has vertical asymptotes where the denominator is $0$ $0$ .

If we are working in degrees

$cos (4 x - 20^{\circ}) = 0$ $cos(4x-20^@) = 0$
$4 x - 20^{\circ} = 90^{\circ} + k 180^{\circ}$ $4x-20^@=90^@+k180^@$ for integer $k$ $k$
$4 x = 110^{\circ} + k 180^{\circ}$ $4x = 110^@+k180^@$ for integer $k$ $k$
$x = {22.5}^{\circ} + k 45^{\circ}$ $x = 22.5^@+k45^@$ for integer $k$ $k$

The graph has vertical asymptotes at $x = {22.5}^{\circ} + k 45^{\circ}$ $x = 22.5^@+k45^@$ for integer $k$ $k$

If we are working in radians or in real numbers

$cos (4 x - 20) = 0$ $cos(4x-20) = 0$
$4 x - 20 = π^{\circ} + k 2 π^{\circ}$ $4x-20=pi^@+k2pi^@$ for integer $k$ $k$
$4 x = (π + 20) + k 2 π$ $4x =(pi+20)+k2pi$ for integer $k$ $k$
$x = \frac{π}{4} + 5 + + k \frac{π}{4}$ $x = pi/4+5++kpi/4$ for integer $k$ $k$

The graph has vertical asymptotes at $x = \frac{π}{4} + 5 + + k \frac{π}{4}$ $x = pi/4+5++kpi/4$ for integer $k$ $k$

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Question #342c3

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