Question #342c3

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Answer 1 · 2017-08-21T12:45:17

Please see below.

#y = 2tan(4x-20) = (2sin(4x-20))/cos(4x-20)#

has no horizontal asymptottes. (There is no limit as #xrarr+-oo#.),
and has vertical asymptotes where the denominator is #0#.

If we are working in degrees

#cos(4x-20^@) = 0#
#4x-20^@=90^@+k180^@# for integer #k#
#4x = 110^@+k180^@# for integer #k#
#x = 22.5^@+k45^@# for integer #k#

The graph has vertical asymptotes at #x = 22.5^@+k45^@# for integer #k#

If we are working in radians or in real numbers

#cos(4x-20) = 0#
#4x-20=pi^@+k2pi^@# for integer #k#
#4x =(pi+20)+k2pi# for integer #k#
#x = pi/4+5++kpi/4# for integer #k#

The graph has vertical asymptotes at #x = pi/4+5++kpi/4# for integer #k#