Rational Functions

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 .