Evaluating Functions Versus Evaluating Limits of Functions

Question

f(x)= [x-1 when x<0, 1 when x=0, x²-1 when x≥0]

For this function, show that f(0) ≠ lim f(x)

lim

x→0

Answer 1

desmos.com/calculator/wolzypcoax

Answer 2

Take a look at this graph of your piecewise defined function: https://www.desmos.com/calculator/rgqcskbtrh

It shows that the behavior of the graph just left of x = 0 is that it approaches -1.

Also, the behavior of the graph just right of x = 0 approaches -1. Therefore, the limit at x = 0 IS -1.

However, there is a hole (discontinuity) there, because actually the value of f(0) is positive one. It is so clear on the graph that I wish that I could paste the picture here.

The video shows the graph.