Question

how are the graphs of y=|x+2| and y=|x|+2 the same

Answer 1

because "2" is a constant, and does not matter if it belongs or not in the absolute value.
Since absolute value of 2 is equal to "2", and "x" being the variable, enclosed in an absolute value in borh cases.

Answer 2

thank you bruh

Answer 3

they are not the same. Plug in -2 in for x and each function will give a different result. They two are the same only if x is non-negative