For the first, you know that
[tex]\begin{gathered} \text{If} \\ y=f\mleft(x\mright)+c \\ \text{You shift the graph of y=f(x) up by c units} \end{gathered}[/tex]So, g(x)=x^(2) +3 will be to move f (x) = x^(2) 3 units up, to move f (x) = x^(2) 3 units up, as can you see in the graph.
Therefore, the graph of f (x) is shifted 3 units up.
[tex]\begin{gathered} \text{ If} \\ y=f(x-c) \\ \text{ you shift the graph of y=f(x) to the right c units} \\ \end{gathered}[/tex]
