a jump discontinuity. You then need to write and find the limit at that point of discontinuity and jump discontinuity. You also have to find the limit at a point on your piecewise defined function that is continuous. Each limit needs to be justified using the graph and the limit notation. Your piecewise defined function needs to have a beginning and end. That means that the domain cannot go to infinity. You will state the domain and the range using interval notation.
properties:
f is differentiable everywhere
f(x+y)=f(x)f(y)
f(0) doesn't equal 0
f'(0) = 1
Show that f(0)=1
Show that f(x) > 0
Use the limit definition of a derivative to show that f'(x) = f(x) for all values of x