Question

can anyone pls help me with this algebra question
click to see a picture of the problem

Answer 1

The value of k is 6.

The vertex of f(x) is at (4, 1).  The vertex of g(x) is at (-2, 1).  It has been shifted left 6 units.  This means that the value of k must be -6 (when translating a function horizontally, the number we add/subtract is the opposite of what we would normally think; we think of left as negative, but to shift it left, we actually add).

Answer 2

From the given functions, it can be seen that the graph of g(x) represents a shift of 6 units to the left of the graph of f(x).

Given a function, f(x), a shift of k units to the left of f(x) is given by g(x + k).

Therefore, if g(x) = f(x + k), then k = 6.