Question

Question #342c3

Answer 1

Please see below.

Explanation:

`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`