For example, f(x)=x4 or 
the graph will be similar to g(x)=x2 or 
This is because if x is a large number (say 100), f(100)
will be a positive number, and notice that f(-100)>0 too. On the
other hands, f(x)=-x4 or 
the graph will be similar to g(x)=-x2 o
r 
This is because if x is a large number (say 100), f(100)
will be a negative number, and notice that f(-100)<0 too.
Example: Compare f(x)=x2 and g(x)=x4
Two Zeroes
Case 1:
Example: Sketch the graph of 
.
Notice that f touches two zeroes at x=2 and 3. This is because the multiplicities of x=2 and x=2 are equal to 2.
Case 2.
Example: Sketch the graph of 
.
Notice that f is ''crossing'' at x=0 and x=1, but there is a little turn between x=0 and x=1. (It is not quite exactly like y=x4) We do not worry about this until we study ''calculus''.
Three Zeroes
Example: Sketch 
.
Four Zeroes
Example: Sketch 
.