. In common sense, students can
tell that this function may have four roots or less than four. What else
can they know about the function? They can try to dot as many points as
possible. But, it doesn't seem to be economic. Basically, students can know
y=1 when x=1. Is the function 
factored into any linear factor
easily? The following graph is from Algebra Xpressor. Let us think about the differential function 
because it will
give more significant information for the function . The differential
function has two roots x=0, and x=1. So the function has two points
where the derivatives are zero. That is to say, two tangent lines at two
different point are parallel to x-axis. See the next graph of and
.
If x<0 , then vales of the differentiated function (green one) are
all negative. So any tangent line on (where x<0) has a negative
slope. And as x decreases from 0 the lopes of tangent lines should be decreased.
Students can compare these all facts from the above graph. There are three
changes in green graph.