Rational Functions Test Review
Name:
Simplifying Rational Expressions
Simplified form: a rational expression is simplified if its numerator and
denominator have NO common factors.
In order to simplify a rational expression you must _____________ and
_______________.
Simplify the following:
x2  6 x  8
x 2  x  20
x 1
6x2  6
x2  4
x3  8
2y 2  9y  18
4 y 2  6y
Multiplying and Dividing Rational Expression
In order to multiply you must ______________ and ________________.
The first step to dividing rational expression is to _____________________.
Simplify the following:
8 x  32 x 4  x3  2 x 2

x3  x 2 4 x 2  16 x  16
x 2  3x  4 x  6

x 2  3x  18 x3  1
x2  2x  3
  x  3
3x 2  x  2
x  11 x  3 x 2  8 x  33


2 x  10 x 2
x5
x 3
x 2  25
x2  9
x5
Adding and Subtracting Rational Expressions
In order to add or subtract fractions you must have a ____________.
Explain how to determine the LCD.
Simplify the following.
3  4n
2

n  3n  10 n  5
2
x
3

x  9 x  x  3
2
x 3
x5
 2
2x 1 2x  9x  5
Graphs of Rational Functions
Explain how to determine the vertical asymptote of a rational function.
Explain how to determine the horizontal asymptote of a rational function.
For each function below determine the vertical and horizontal asymptotes,
domain and range.
f ( x) 
5
x
f ( x) 
V.A. ________
H.A. ________
Domain ______
Range _______
2 x2  5x  3
x2  9
V.A. _______
H.A. _______
Domain _______
Range _______
Graph the following rational functions.
f ( x) 
x 2
x 3
f ( x) 
1
3
x2
 y
 y







    


x





    









x





Types of Variation
Write the equation being described by each of the following statements.
1. Y varies jointly as W and X. ______________________________
2. Y varies directly as the square of X. _____________________________
3. R varies inversely as T and directly as S.__________________________
4. Y varies inversely as the square of X. ___________________________
5. The volume, v, of a balloon is directly proportional to the cube of the
balloon’s radius, r. ______________________________
6. The weight, w, that a column of a bridge can support varies directly as the
fourth power of its diameter, d, and inversely as the square of its length, l.
______________________________
Write a variation statement for the following models in which k is the constant of
variation. Then solve.
Boyle’s Law states that, for a fixed amount of gas, the volume of the gas at a constant
temperature is inversely proportional to the pressure. If a certain gas occupies 9.84 liters
at a pressure of 50 centimeters of mercury (cm Hg), what is the approximate pressure
when the volume is increased to 12 liters?