Question

The graph of F(x), shown below, has the same shape as the graph of G(x) = x3 - x2, but it is shifted to the left 2 units. What is its equation?

Answer 1

$G(x)=x^3-x^2$

To move a graph to the left or to the right you use the next formula:

$\begin{gathered} f(x)=x \\ f(x-c)=x-c\text{ (Right)} \\ f(x+c)=x+c\text{ (Left)} \end{gathered}$

c is the units the graph is moved.

Then, f(x) is:

$F(x)=(x+2)^3-(x+2)^2$