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# Rational Functions

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### Rational Functions

1. 1. Rational FunctionsBy : Ca’lais R. & Antoin M. Period 2 Algebra 2
2. 2. Rational Function•A function that can be writtenas two polynomials with integral coefficients
3. 3. • 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 ).
4. 4. • 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.
5. 5. Graphing & Equations• Insert equation into “y equals” on your calculator
6. 6. • 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
7. 7. 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?
8. 8. Rational Functions
9. 9. Rational Functions
10. 10. •Thanks for watchingCa’lais Rubin & Antoine Malveaux