Rational FunctionsBy : Ca’lais R. & Antoin M. Period 2 Algebra 2
Rational Function•A function that can be writtenas two polynomials with integral coefficients
• Numbers that can be written as fractions are called rational numbers. Heres a small list: 1/2, 4/7 and 2/9 are samples ofrational numbers. The numbers 0.5, .571428......., .2222.... are all rational numbers because they are exactly the same as the fractions just listed ( and the definition of rational means they can be rewritten as fractions ).
• Express y = x^2 - 3x - 2/3x - 2 in standard form.• Since y = f(x) and f(x) = y, we can replace y with f(x). • Answer: f(x) = x^2 - 3x -2/3x - 2.
Graphing & Equations• Insert equation into “y equals” on your calculator
• x = 0: y = (0 + 5)/(0 – 1) = 5/–1 = –5 y = 0: 0 = (2x + 5)/(x – 1) 0 = 2x + 5 –5 = 2x –2.5 = x
Appliance Average cost/year in electricity Home computer $9 Television $13 Microwave $13 Dish washer $51 Clothes Dryer $75 Washing Machine $79 Refrigrator $92• a) If we assume that a new refrigerator costs $550, determine the total annual cost for a refrigerator that lasts• for 15 years. Assume the only costs associated with the refrigerator are it purchase cost and electricity.• b) Develop a function that gives the annual cost of a refrigerator as a function of the number of years you own• the refrigerator.• c) Sketch a graph of that function. What is an appropriate window?• d) Since this is a rational function, determine the asymptotes of this function?• e) Explain the meaning of the horizontal asymptote in terms of the refrigerator.• f) If a company offers a refrigerator that costs $1200, but says that it will last at least twenty years, is the• refrigerator worth the difference in cost?