Question

f(X)=-4tan4pi(X+4)-2, what is the vertical displacement and phase shift?

Answer 1

Given some function \(f(x)\), a phase shift of \(c\) is given by \(f(x-c)\) and a vertical displacement of \(d\) is given by \(f(x)+d\).

In this case, \(f(x)=-4\tan 4\pi x\).

Note that \(f(x-c)=-4\tan4\pi(x-c)\). This means that you'll have to distribute the \(4\pi\):
\[f(x-c)=-4\tan(4\pi x-4\pi c)\]