Given the graph of the function fx x3 3x find a formula fo

Given the graph of the function f(x) = -x3 + 3x; find a formula for g(x).

A) g(x) = f(x - 3)         B) g(x) = f(x + 3)         C) g(x) = f(x) - 3          D) g(x) = f(x) + 3

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Solution

f(x) = -x^3 + 3x

We can see the graph of g(x) is the graph of f(x) shifted to left by 3 units:

So, g(x) = f( x -3) = -(x-3)63 +3(x-3)

Option A