Sketch the graph of a function y = f(x) with all of the following properties.
a. f '(x) > 0 for −8 ≤ x < 1
b. f '(2) = 0
c. f '(x) > 0 for x > 2
d. f(2) = −1 and f(0) = 1
e. lim x→−[infinity] f(x) = 0 and lim x→[infinity] f(x) = [infinity]
f. f '(1) does not exist. Since we are given in
(d) that f(2) = −1 and f(0) = 1, the points (2, −1) and (x, y) = ? are on the graph of f(x).