Question

The graph of g(x) is a transformation of f(x)=x^3. Write the equation of g(x).

Answer 1

`g(x) = f(x - 1) + 3 = x^3 - 3x^2 + 3x + 2`

Explanation:

g(x) is f(x) moved one to the right, as well as moved 3 up (The inflection point was (0,0) on f(x), and is now at (1, 3) at g(x)).

Therefore, to move f(x) one to the right, we must subtract 1 from x, making it
`f(x - 1)` , and add 3 to the y value, making it
`f(x - 1) + 3`

`g(x) = f(x - 1) + 3\\\to g(x) = (x - 1)^3 + 3\\\to g(x) = x^3 -3x^2 + 3x - 1 + 3\\\to g(x) = x^3 - 3x^2 + 3x + 2`