In general, the standard translation of a function f into another function g can be obtained as follows:
g(x)=f(x-h)+k
where
h=horizontal translation (to the right), and
k=vertical translation (upwards).
The left graph is f(x)=x^3-4x
(because the initial value = constant term = 0)
Since g(x) is the simple translation of f(x), i.e. without distortion, all maxima and minima are translated by the same values h and k.
We see that the maximum (-1,3) has been translated to (2,1), through the difference (2-(-1), 1-3) = (3,-2)
We know that h=3 (horizontal translation) and k=-2 (vertical translation).
HOWEVER, the definition of h and k for this question is
g(x)=f(x+h)+k,
so we must reverse the sign of (our) h due to the difference in definition.
According to the question definition of h and k, h=-3, and k=-2.
Therefore the product hk = (-3)(-2) = 6
Note: if we use a different set of corresponding points, the results would be the same.
