Question

Tables of values for f(x) and g(x) are given below. Write g(x) as a transformation of f(x).

Answer 1

From the given table, it is clear that if
$x_{g} = x_{f} + 8$
then the values of f and g match.

Therefore
f(x+8) = g(x)
or
g(x) = f(x+8)

The required transformation is a left shift in x by -8 units for f(x).
A composite graph of f(x+8) and g(x) confirms that the transformation is correct.