Part A
To shift the curve 3 units to the right, we'll replace x with x-3. What this does is move the xy axis 3 units to the left. If we held the curve in place as the axis moves, then it gives the illusion the curve is moving 3 units to the right.
[tex]f(x) = x^2 + 5\\\\f(x-3) = (x-3)^2 + 5\\\\g(x) = (x-3)^2 + 5\\\\[/tex]
Do not expand out the (x-3)^2 term, because you want to keep the function in vertex form. The old vertex of (0,5) moves three units to the right to arrive at (3,5)
==============================================================
Part B
We use the same idea as before. This time we're moving the curve 10 units to the left, so we'll replace x with x+10
[tex]f(x) = x^2 + 5\\\\f(x+10) = (x+10)^2 + 5\\\\g(x) = (x+10)^2 + 5\\\\[/tex]
