Final answer:
The appropriate viewing window for the function f(x) = -|x + 5| + 12 is -15 ≤ x ≤ 5, 0 ≤ y ≤ 12, which captures the significant part of the 'V' shaped graph created by this absolute value transformation.
Step-by-step explanation:
When graphing the function f(x) = -|x + 5| + 12, it is important to consider the properties of the function to choose the most appropriate viewing window on your graphing calculator. The function is a transformation of the absolute value function, which means it has a 'V' shape. The vertex of this 'V' happens at x = -5, because that's when the expression inside the absolute value turns from negative to positive. As for the y-values, intuitively f(x) ranges from 12 (when x+5 is 0 or x=-5) downto negative infinity technically, but we are capped at y=12 due to the vertical shift and the negative sign flips the 'V' upside down. However, for practical graphing purposes, it's sufficient to see the portion where the function significantly changes, so we can set the window to capture from y=12 down to slightly below the vertex.
The correct answer to the question is thus Option a) -15 ≤ x ≤ 5, 0 ≤ y ≤ 12 as it fully encompasses the significant part of the graph where the transformation occurs (from the vertex and to the left of it).