Q:

Point B = (-1, -1) belongs to the graph of the function h, where h(x) = f(x - 2) + 3. Determine the coordinates point A belonging to the graph of the function f.

Accepted Solution

A:
The function h(x) is a transformation of the function f(x). Specifically, h(x) = f(x - 2) + 3 represents a shift of the graph of f(x) 2 units to the right and 3 units up. So, to find the corresponding point A on the graph of f(x), we need to reverse these transformations. This means we shift the x-coordinate of point B 2 units to the left and the y-coordinate 3 units down. Therefore, the coordinates of point A are (-1 - 2, -1 - 3) = (-3, -4). So, point A = (-3, -4) belongs to the graph of the function f.