Sketch a graph of a function f(x) that has the following properties

a. f(x) is continuous and differentiable everywhere except at x = 3, where it has a

vertical asymptote

b. f(x) has a horizontal asymptote of y = 1

c. f(2) = 0

d. f(0) = 4

e. f

(x) > 0 on the interval (, 3) (3, 2)

f. f

(x) < 0 on the interval (2, )

g. f

(2) = 0

h. f

(x) > 0 on the intervals (, 3) (4, )

i. f

(x) < 0 on the interval (3, 4)

j. f(x) has an inflection point at (4, 3)