With an understanding of vertical and horizontal translation, the point (0, 0) on the graph of f(x) corresponds to (-5, -6) point on the graph of g(x).
What is vertical and horizontal translation?
If y = f(x), then y = f(x) + k gives a vertical translation. The translation k moves the graph upward when k is a positive value and downward when k is negative value.
If y = f(x), then y = f(x-h) gives a horizontal translation. The translation h moves the graph to the left when h is a positive value and to the right when h is negative value.
On comparing [tex]g(x) = (x + 5)^{3} - 6\\[/tex] with the definition of horizontal and vertical translation, there is a 5 unit horizontal translation to the left. This implies that abscissa 0 shifts to (0 - 5) = -5 abscissa. Also, there is a 6 unit downward vertical translation. Ordinate 0 shifts to (0 - 6) = -6 ordinate.
The new coordinates become ( -5, -6).
Learn more about horizontal and vertical translation here
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