[**Use Maple to graph the following functions: f(x)=3x3+4, f(x)=-2x3-4, f(x)=3(x+3)3-1, and f(x)=-4(x-3)3+1.]
(1) If a>0, then the tails of graph of y=f(x) look like that of y=x3. For example, when x=100, y is a large positive number, and when x=-100, y is a negative large number.
(2) If a<0, then the tails of graph of y=f(x) look like that of y=-x3.
Zeroes of cube funtions
For a cube function, we have the following three possiblities:
(1) One zero: For example, f(x)=ax3+b
or
[**Use Maple to graph the following functions: f(x)=3x3+4,
f(x)=-2x3-4,
f(x)=3(x+3)3-1,
and f(x)=-4(x-3)3+1.]
(2) Two zeroes: For example, 
,
g(x)=-3(x-3)2(x-2).
We call x=2 a zero of f with multiplicity 2 , and x=3
a zero of g with mulitplicity 2. If it is a muliticity 2, then the
x intercepts will be adjacent to the x-axis. Use "Maple" to graph
f
and g.
(3) Three zeroes: For example, 
The zeroes of f are x=1,x=2,x=3. Since the
coefficient of a is positive, the tails of f should look
like y=x3.
Signs of f(x)
If we know when f(x)>0 or f(x)<0, it should help us to graph f.
Example 1. Let
Find the intervals for which f(x)>0 and f(x)<0.
By knowing when f(x)>0 and f(x)<0 will help us to graph of f.
Case 1: Note that f(x)>0 if 
we can use short cut to solve this since it is a standard form, it is when
x
is in the intervals 
Case 2: Note that f(x)<0 if 
it is when x is in the intervals 
Use "Maple" to verify this.
Example 2: Let 
Find the intervals for which f(x)>0 or f(x)<0.
Case 1: If 
if 
which means x is in the intervals
Case 2: If 
if 
,
which means x is in the intervals
Use Maple to verify this.