Question

The graph of y=x is shifted up 2 units and 3 units to the left. Which is the equation of the translated function?

Answer 1

Check the picture below.

$y = x\implies y = \stackrel{A}{1}(\stackrel{B}{1}x+\stackrel{C}{0})+\stackrel{D}{0} \\\\\\ \begin{cases} \stackrel{\textit{2 units up}}{D=+2}\\\\ \stackrel{\textit{3 units left}}{C=+3}\\ B=1 \end{cases}\qquad \implies y = \stackrel{A}{1}(\stackrel{B}{1}x\stackrel{C}{+3})\stackrel{D}{+2}\qquad \implies y=(x+3)+2$