Grade 12: Rationals Task 2

What do you notice?  What do you wonder?

What would happen if the red function were the numerator and the blue function were the denominator?  What do you know about the quotient function?

What would happen if the blue function were the numerator and the red function were the denominator?  What do you know about the quotient function?

We had a look at the problem in class today. We realized that we don’t need the numbers on the graph, or the equation even, to get an idea of a rational function’s graph.

We looked for places where the denominator function is zero. That’s where we’d find vertical asymptotes. We looked for where the numerator function is zero, and that’s where the zeros of the rational function will be. We looked at the signs, and relative values of the numerator and denominator and strategically looked to each side of the asymptotes, and at the end behaviours.

some groups had time to look at the rational function of “blue” divided by “red” as well. The function looks very different at the ends. We know that when the degree of the numerator is less than the degree of the denominator, the function will have a horizontal asymptote at 0. Above, the numerator had a degree that was 2 greater than the denominator, which led to a parabolic asymptote.