Think of a rational function. The value of y is 0 when
x is 0. Again let's differentiate the function. Then, we have . We can have two points, (1,0) and (-3,0) from , and in those
points the function are supposed to change the signs of slopes
of tangent lines. The following graph is and y=1. Students
can know that the horizontal line y=1 is asymptote.
Let us analyze the differential function, with a graph from Algebra Expressor. Can you see the relation between and?
The next picture is a combination of , , and y=1.