Which description best explains the domain of (g circle f) (x)? A) the elements in the domain of f(x) for which g(f(x)) is defined
B) the elements in the domain of f(x) for which g(f(x)) is not zero
C) the elements in the domain of g(x) for which g(f(x)) is defined
D) the elements in the domain of g(x) for which g(f(x)) is not zero

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  A) the elements in the domain of f(x) for which g(f(x)) is defined

Step-by-step explanation:

(g circle f)(x) means g(f(x)). In order for a value (x) to be in the domain of this function, f(x) must be defined. That is, x must be in the domain of f(x). In addition, g(f(x)) must be defined.

These requirements are expressed in choice A.

The answer is y=(x+1)2-1. The x plus one causes the whole parabola to actually shift to the left by one unit rather than to the right. The subtraction of one causes a vertical shift down by one unit, so the vertex moves from (0,0) to (-1,-1).