Write the equation of the transformed graph of tangent with period 4 that has been shifted vertically up 3 units

Our parent function:

y = tan x

Let's apply the vertical shift now:

y = 3 + tan x

Now the period. This is a little tricky because we have to remember that the period is equal to π/b, because tangent functions normally have a period of π, and the b is the value placed in front of the x.

In this case, that value would have to be π/4

π / (π/4) = 4

Therefore, our b-value is π/4 and our final equation is as follows:

y = 3 + tan (π/4) x