We are given the function:
[tex]f(x)=x-2+3=x+1[/tex]And we want to know a transformation of it after it is shifted one unit left, and 2 units down.
We remember that if we have a function f(x), we get the following transformations:
[tex]\begin{gathered} f(x+c)\Rightarrow\begin{cases}\text{moves to left if }c>0 \\ \text{moves to right if }c<0\end{cases} \\ f(x)+c\Rightarrow\begin{cases}\text{moves up if }c>0 \\ \text{moves down if }c<0\end{cases} \end{gathered}[/tex]Thus, as we want to move one unit left, and two units down, we have to get a expression for:
[tex]f(x+1)-2[/tex]As:
Thus, replacing on the function we get:
[tex]\begin{gathered} f(x+1)-2=(x+1)+1-2 \\ =x+2-2 \\ =x \end{gathered}[/tex]This means that if we move the function one unit left, and two units down, we get the function g(x)=x.
