Final answer:
The equation that represents a tangent function with a domain of all Real numbers such that x is not equal to pi over 2 plus pi times n, where n is an integer, is y = tan(x). The values that make x equal to pi/2 + pi*n will result in vertical asymptotes.
Step-by-step explanation:
The equation that represents a tangent function with a domain of all Real numbers such that x is not equal to pi over 2 plus pi times n, where n is an integer, is y = tan(x).
The tangent function has a period of pi, so the values that make x equal to pi/2 + pi*n will result in vertical asymptotes. These values make the tangent function undefined.
For example, if n=0, the equation becomes y = tan(x), and the x-values that should be avoided are x = pi/2. If n=1, the equation becomes y = tan(x), and the x-values that should be avoided are x = pi/2 + pi, x = pi/2 + 2pi, and so on.