Below is the rational function, given in general form ([math]f\left(x\right)=\frac{ax+b}{cx+d}[/math]) as well as transformational form ([math]f\left(x\right)=e+\frac{g}{cx+d}[/math]).[br][br]You can have the application show the asymptotes, and you can adjust [math]a,b,c,[/math] and [math]d[/math]. Adjust these, and see how they affect the graph, and then answer the questions below.

[b]Question 1:[/b] Why is the function called a rational function? What does rational mean in mathematics?[br][br][b]Question 2: [/b]Make the graph in general form ([math]\frac{ax+b}{cx+d}[/math]). Show the equations of the asymptotes, and change [math]a,b,c,[/math] and [math]d[/math]. Write an equation for the vertical asymptote for the function [math]f\left(x\right)=\frac{ax+b}{cx+d}[/math]. Does this apply to the transformational form too?[br][br][b]Question 3:[/b] Hence, what is the domain of the function [math]f\left(x\right)=\frac{ax+b}{cx+d}[/math]?[br][br][b]Question 4:[/b] Can you find any patterns for the horizontal asymptote? Try in transformational form. Write an equation for the horizontal asymptote for the function [math]f\left(x\right)=e+\frac{g}{cx+d}[/math].[br][br][b]Question 5:[/b] Hence, what is the range of the function [math]f\left(x\right)=e+\frac{g}{cx+d}[/math]?[br][br][b]Question 6: [/b]In your notebook, consider the function [math]f\left(x\right)=\frac{ax+b}{cx+d}[/math] for [math]c\ne0[/math]. Show that [math]\frac{ax+b}{cx+d}=\frac{a}{c}+\frac{b-\frac{ad}{c}}{cx+d}[/math].[br][br][b]Question 7:[/b] Hence, find the equation of the horizontal asymptote for the function [math]f\left(x\right)=\frac{ax+b}{cx+d}[/math].