Rational functions are functions that can be written as the ratio of two polynomials with integer coefficients. Rational numbers are numbers that can be written as fractions, such as 1/2, 4/7, and 2/9. To write a rational function in standard form, you can replace the variable in the function with f(x). For example, writing y = x^2 - 3x - 2/3x - 2 in standard form is f(x) = x^2 - 3x -2/3x - 2. Graphing a rational function involves inserting the equation into the y-equals function on a calculator and finding x-intercepts. The asymptotes of a rational function can also be determined.

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

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

3. • 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, .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. • 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. Graphing & Equations
• Insert equation into “y equals” on your
calculator

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

9. 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?

10. Rational Functions

11. Rational Functions

12. •Thanks for watching
Ca’lais Rubin & Antoine
Malveaux