Module 7: Rational Functions and Function Operations

 

Did You Know?

Although any symbol can be used to represent a function or variable, some letters are more likely to be used than others. It is common in mathematics to pick particular letters for different jobs. This can make reading the math a bit easier because it can give you a clue to what the letter represents. Here are some common uses of lowercase Latin letters.

 

a, b, c, d parameters (unspecified constants)
e Euler’s number (2.718…)
f, g, h functions
i the imaginary unit (i2 = −1), integer variable
j, k integer variables
l avoided because it looks like a 1
m, n integer variables
o avoided because it looks like a 0
p unspecified prime number, polynomial function
q unspecified quotient, polynomial function
r unspecified remainder, variable that is a radius
s variable that is an arc length or speed
t variable that is a time
u, v, w, x, y, z variables that are real numbers

 

In addition, many capital letters, Greek letters, and other symbols have typical uses. The context will also give clues to how different symbols are used.



In Try This 2 you may have found that adding and subtracting functions is quite simple. You just add or subtract them!


In Try This 2 you saw that if f(x) = x2 + x and g(x) = 3x − 1, then

 

 
 and



textbook

For some additional examples of how functions can be added or subtracted, read “Example 1” on pages 476 and 477 of the textbook or “Example 2” on pages 478 and 479.

 

 

Self-Check 1

 

Complete questions 1.a., 1.d., 2.a., 2.d., 3.a., 3.c., 9.b., 9.c., 10.a., and 11.d. on pages 483 and 484 of the textbook. Answer