For [math]f(x) = 3x^2 + 13x – 10[/math] and [math]g(x) = x + 5[/math], find [math]\Big(\frac{f}{g}\Big)\Big(x\Big)[/math]. What type of function is the quotient of [math]\Big(\frac{f}{g}\Big)\Big(x\Big)[/math]? Are there restrictions on the domain and range of the function [math]\Big(\frac{f}{g}\Big)\Big(x\Big)[/math]?

[list=1][br][*]Since the functions are being divided, write the functions [math]f(x)[/math] and [math]g(x)[/math] as a fraction.[br][/*][*]Factor the quadratic function, [math]f(x)[/math].[br][/*][*]Simplify the equation and define the type of equation of the simplified form.[br][/*][*]Look at the original fraction to see if there are restricted values on the domain.[br][/*][/list][br][br]This applet is provided by Walch Education as supplemental material for their mathematics programs. Visit [url=http://www.walch.com/]www.walch.com[/url] for more information.