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Math 111 Name Key Grp Rational Functions 1 GrpAct 10 Prerequisite Skills lowest terms domain restrictions Factoring Finding the degree of a polynomial Find the leading coefficient of a polynomial Key Terms rational function rational equation vertical asymptote horizontal asymptote hole radical equation Sections 4 6 4 7 Learning Outcomes Identify vertical and horizontal asymptotes as well as roots and holes for rational functions Solve rational and radical equations Translate radical expressions to rational exponents 1 A local manufacturing company has cost and revenue functions C x 31 2x 15000 and R x 69 9x where x is the number of units produced It costs 31 20 to produce one unit and the company has fixed costs of 15000 The product sells as 69 90 per unit From these we have a profit function of P x R x C x 69 9x 31 2x 15000 38 7x 15000 Total Profit Units Produced P x 38 7x 15000 For this company the average profit is given by P x x x The company calculates their average profit P as a Determine each of the following and explain what they represent in the context of this problem P 1000 23 700 P 1000 23 70 P 10000 37 20 P 100000 38 55 b The graph of P x is given Label the axes A v e c P x has a horizontal asymptote of y 38 7 Explain what this asymptote represents in the context of this problem d This function has an x intercept Give the coordinates of that x intercept and explain why it occurs in the context of the problem P r o f i t 358 0 Number of items produced This is the Break Even Point i e make fewer items and you loose money or make more and you make a profit At a production rate of 358 units the cost is equal to the revenue 2 A big part of learning about rational functions is understanding how to identify asymptotes and intercepts The last function we saw had both a horizontal and a vertical asymptote In this problem we will look a little more closely at vertical asymptotes You should have an understanding of what a vertical asymptote is and why one occurs