Below is the rational function, given in general form () as well as transformational form ().
You can have the application show the asymptotes, and you can adjust and . Adjust these, and see how they affect the graph, and then answer the questions below.

Question 1: Why is the function called a rational function? What does rational mean in mathematics?
Question 2: Make the graph in general form (). Show the equations of the asymptotes, and change and . Write an equation for the vertical asymptote for the function . Does this apply to the transformational form too?
Question 3: Hence, what is the domain of the function ?
Question 4: Can you find any patterns for the horizontal asymptote? Try in transformational form. Write an equation for the horizontal asymptote for the function .
Question 5: Hence, what is the range of the function ?
Question 6: In your notebook, consider the function for . Show that .
Question 7: Hence, find the equation of the horizontal asymptote for the function .