A Sum as Input

Here the input $k-1$ goes into $g\left(x\right) = {x}^{2}+2x$. Each x becomes $\left(k-1\right)$, in brackets.

• $g\left(k-1\right) = {\left(k-1\right)}^{2}+2\left(k-1\right)$.
• Multiply out: ${k}^{2}-2k+1+2k-2$.
• Add the like terms, the ones with the same power of k: ${k}^{2}-1$.

So an expression works as an input, like a number. Watch the square: ${\left(k-1\right)}^{2}$ has a middle term, -2k. You find the rule of the moved curve $y = f\left(x-3\right)$ the same way.