Which of the following points must lie on the graph?

Explanation:

The point (0,4) is on the f(x) curve. This means that when x = 0, f(x) = 4. Or f(0) = 4.

If we plugged x = 4 into f(x-4), then it becomes f(x-4) = f(4-4) = f(0).

g(x) = -f(x-4) + 1

g(4) = -f(4-4) + 1 ... plug in x = 4

g(4) = -f(0) + 1

g(4) = -4 + 1 ... replace f(0) with 4

g(4) = -3

So we can see that the input x = 4 leads to the output g(x) = -3.

The point (4,-3) is on the g(x) curve.