A trigonometric function g has been vertically stretched and horizontally shifted. It satisfies the following conditions:
• Its graph has vertical asymptotes at x=−4π+nπ, where n∈Z.
• It passes through the point (4π,0).
• For every x in its domain, g(x) is exactly twice the corresponding value of the usual tangent function.
(a) Obtain a simplified equation for g(x).
(b) Sketch one complete period of g(x).
(c) Write the domain and range of g.