**Unformatted text preview: **MAC1105: Rational functions A function that represents a ratio of polynomials is called a rational function; Polynomial R(x) Polynomial = . In this class we will study rational functions of the form f(x) Linear function R(x) g(x) Linear function = = = = = = = = . The graphs of these particular rational functions are called hyperbolas . The study of hyperbolas in general is a topic from pre-calculus. Ex : Let 3x 12 R(x) x 2 + =- . We will graph this function by determining all of its intercepts and asymptotes. Intercepts: x : We find the x-intercept by setting the numerator equal to 0 and solving the equation 3x 12 3x 12 x 4 + = → = - → = - + = → = - → = - + = → = - → = - + = → = - → = - . So the x-intercept is at the point ( 4,0)- . y : We find the y-intercept by evaluating 3(0) 12 12 R(0) 6 (0) 2 2 + = = = - = = = - = = = - = = = --------- . So the y-intercept is at (0, 6)- ....

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