Originally Posted by

**PurpleLeprechaun** One of our homework problems asks us to graph a functio given several characteristics, but I don't really understand how to do it.

Suppose that a function f has the following characteristics

i) f(0)=0

ii) f continuous except at x=2

iii) lim f(x) = +infinity

x2

iv) lim f(x)=0

x-infinity

v) lim f(x)=3

x+infinity

vi) f ' exists except at x=2, -1

vii) f ' > 0 if -1 is less than or equal to x is less than or equal to 2

viii) f ' < 0 if x< -1 or x> 2

ix) f '' < 0 if x <0 and x is not equal to -1

x) f '' > 0 if x > o and x is not equal to 2

Sketch the graph of the function f.

does vi mean that there are asymptotes at those values on f? If so, how do you reconcile that with the horizontal asymptote at 0? I don't really understand how to apply any of the f ' or f '' characteristics listed to the graph of f, either.

Could someone point me in the right direction? Thanks.