Graph f(x) = tan(4x) + 3. Find the amplitude, period, phase shift, and vertical shift of the function.

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tiburtius | High School Teacher | (Level 2) Educator

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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. 

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