This Desmos link shows what is happening graphically when you construct a table of values to investigate a limit. Desmos is also very useful for quickly evaluating functions at several inputs (just define f(x)=……, and then type f(0.01), f(0.001), etc. in lines below it).
This Desmos graph gives an interactive way to think about average rates of change in the context of examples from physics and economics. You should try changing the definition of the function, and see how you can interpret the examples in that case.
This Desmos graph shows you how to graph piecewise functions in Desmos. You can also experiment with the slope and intercept of a line piece, and try to connect it to a parabola piece in a smooth way.