A continuous function that is -1 for x -0.1, 1 for x 0.1, and is

Question:

A continuous function that is -1 for x ≤ -0.1, 1 for x ≥ 0.1, and is linear for -0.1 < x < 0.1.
We can build different continuous approximations of signum (the function giving the sign of a number) as follows. For each, case
a. Graph the continuous function.
b. Find the formula.
c. How close would the input have to be to 0 for the output to be within 0.1 of 0?