Question

Write the equation of the transformed graph of tangent with period 4 that has

been shifted vertically up 3 units. (3 points)

Answer 1

g(x) = 3 + tan(πx/4)

Explanation:

A tangent function has a period of π. In order to make it have a period of 4, it needs to be stretched horizontally by a factor of 4/π. A function is stretched horizontally by a factor of k by replacing x with x/k.

In order for the function to be shifted vertically up by 3 units, 3 must be added to the function value. That is, the transformed function becomes ...

g(x) = tan(x/(4/π)) +3

g(x) = tan(πx/4) +3