Question

The graph of the parent function f(x) = x3 is translated to form g(x) = (x – 7)3 + 9. The point (0, 0) on the graph of f(x) corresponds to which point on the graph of g(x)?

Answer 1

recall that, for a generic function f(x),
g(x) = f(x-h) + k
g(x) represents a horizontal translation of f(x) by h units and vertical translation by k units.
if h is positive, it moves h units to the right
if h is negative, it moves h units to the left

if k is positive, it moves k units up
if k is negative, it moves k units down

try to apply this logic to f(x) = x^3 and g(x) = (x-7)^3 + 9 to figure out what your h and k values are, and what the translation is. then apply that same translation to (0,0)