Graph f(x) = tan(4x) + 3. Find the amplitude, period, phase shift, and vertical shift of the function.
In a function `g(x)=a tan(b x+c)+d` , `a` is amplitude, `b` is circular frequency, `c` is phase shift and `d` is vertical shift of the function. In your case `a=1,b=4,c=0,d=3.`
Hence the amplitude is `a=1.`
We can calculate the period by dividing the period of `tan x` (which is equal to `pi` ) by circular frequency. Hence period is `P=pi/4.`
Phase shift is `c=0.`
Vertical shift is `d=3.`
In the picture below blue curves represent your function `f` while red lines are asymptotes.