The following are procedures to draw a graph.
f'(x)>0 if |x|<2, f'(x)<0 if |x|>2, f'(2)=0, limit as x approaches infinity=1, f(-x)=-f(x), f"(x)<0 if 0<x<3, f"(x)>0 if x>3.
if the nature of the this function following |x|, what confuses me is how can i draw a graph that is concave downward between 0 and 3, and concave upward greater than 3 when the lines have to be straight.
-I did try drawing it but i am not sure if it's right. I begin at the origin and draw a line concave downward up to 2, from here should the turning point be pointy like on an |x| graph or smooth like on a parabola? then it continues to be concave downward with a negative gradient until it gets to 3 then it becomes concave upward.
-Also, for the limit as x approaches infiinity=1, does that mean there is a horizontal asymptote at y=1.