Rational Functions By : Ca’lais R. & Antoin M. Period 2 Algebra 2

Rational Function A function that can be written as two polynomials with integral coefficients

Numbers that can be written as fractions are called rational numbers. Here's a small list: 1/2, 4/7 and 2/9 are samples of rational numbers. The numbers 0.5, , 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

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? ApplianceAverage cost/year in electricity Home computer$9 Television$13 Microwave$13 Dish washer$51 Clothes Dryer$75 Washing Machine$79 Refrigrator$92

Rational Functions

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