Rational Function Inverse - A Visual Approach
- Jennifer Silverman
This applet is really for teachers, because it shows my final thinking. See below for my thoughts on student use.
Working with students
With students, I would encourage an exploration of the reflections of the function and of each intercept and asymptote. Then they'll need a little algebraic thinking to refine the values of the parameters. Here's how I approached it - like a puzzle! It also helped to notice how similar the graphs were, so I knew the equations would be similar, too. Quick questions: 1. How do you you find the value of x when y=0? 2. How do you make y=1 when x=0? 3. How do you make y=-2 when x gets infinitely big or small? 4. How do you verify that y gets infinitely big or small when x=-1.5? Quick answers: 1. Set numerator to zero. 2. The constants must be equal. 3. The numerator's x-coefficient is twice the denominator's. 4. Set denominator to zero.