This is a fourth power function . 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.