Chapter 5: Rational Numbers and Rational Functions
Day
1
2
Subject Matter of the Day
 Lesson 5.1 Rational Numbers
o Rational (iff) If and only if
b
o Identity = an equation that is true for all values for
which both sides are defined
o Check by the domain of the identity
o Compound function = compound fraction
o Lowest Common Denominator
 Problems
Page Examples
1 29
287
6-13,17
 Lesson 5.2 Rational Expressions
o Rational Polynomial
where
o Restrictions: Domain errors
by zero or
in denominator
o Lowest Terms: factor and cancel out polynomials but
do not forget restricted or excluded values
 Problems
Page Examples
1 28
293
6,8,16
3
 Ms 5.1 to 5.2
4
 Lesson 5.3 Reciprocals of Power Functions
o New Limit notation :
 a+ coming from the right
 a- coming from the left
o
o
o Translations: even vs. odd
 Problems
Page Examples
1 18
298
7,8
 Lesson 5.4 Rational Functions
o
p(x) and q(x) are polynomials in the
5
domain of f(x)
o Removable Discontinuity: point when the zero of q(x)
is a zero of p(x) (point of discontinuity)
o Essential Discontinuity: asymptote when the zero of
q(x) is not a zero to p(x); the zero then becomes the
line of discontinuity
 Problems
Page Examples
1 22
305
3,4,5,10
6
7
8
 Lesson 5.5 End Behavior of Rational Functions
o For polynomials: factor out an xn from each term
o
=
o Equal degrees in numerator and denominator
 Graph
 Divide each term by xn (highest degree term)
then take limit
 Long division then take limit of quotient
o Numerator higher degree then denominator
1. Graph
2. Long division then take limit of the quotient
o Denominator higher degree then numerator
1. Graph
2. Similar to reciprocal of power function limit
 Problems
Page Examples
1 19
320
4,5
 Ms 5.3 to 5.5
 Lesson 5.6 Irrational Numbers
o Irrational: cannot be written as a ratio of two other
numbers
o Conjugates: rationalizing the denominator
 Difference of squares
 Fancy one
 Problems
Page Examples
1 24
320
7,13,18

Repeating decimals need to use a power of 10 equal to
the number of repeating places
 Lesson 5.7 The Tangent, Cotangent, Secant, and Cosecant
Functions
o Review
o
9
o Reciprocal Trig Functions
o
o
o
10
 Problems
Page Examples
1 19
324
2,3,12
 Lesson 5.8 Rational Equations
o Solve using algebra (BEWARE extraneous solutions)
 Problems
Page Examples
1 28
331
5,8,16
11
12
13
 Ms 5.6 and 5.8


Chapter 5 Review
o Worksheet
Test Chapter 5
o Test Corrections will be due two days later
Semester Exams:
1
 Review Book Quizzes Chapter 1,2, & 3
2
 Review Book Quizzes Chapter 4 & 5