The famous irrational numbers

The most famous irrational number is pi because it pops up in so many different situations. Probably the next most famous one is 'e', the base of natural logarithms. The square root of 2 is also right up there.

The size of the shift from function f to function g is 12 units (downward).
your graph looks correct.



given that f(x) = 2^x and g(x) is some sort of vertical shift of f, we can form this table with the values of f(x) = 2^x

   

we can see that every value of function f has been shifted 12 units downward for the corresponding value of function g.
therefore, g(x) = 2^x - 12.

if we want to plot something that's is only shifted half as much as g, that's the graph of f shifted 6 units downward. we have to be graphing out y = 2^x - 6.

your graph looks correct as it does indeed shift every original point of the parent function f down 6 units.