Download Summary of changes in Math 64 effective Fall 2014:

Summary of changes in Math 64 effective Fall 2014:
We now start the course by introducing functions. Additionally, we cover the review of linear inequalities, using
inequalities in business applications, compound inequalities, and solving absolute value inequalities as well as the
absolute value equations. Exponential decay, conic sections, and solving non-linear systems of equations are added as
optional topics.
INTRODUCTORY AND INTERMEDIATE ALGEBRA 4TH EDITION BY ROBERT BLITZER
TOPIC
SECTION OBJECTIVES/NOTES
STUDENTS SHOULD BE
PROFICIENT IN THE SKILLS
REPRESENTED BY THE
FOLLOWING RANGE OF ITEMS
IN THE BLITZER PROBLEM SETS
Introduction
8.1
Full coverage
1-23 odd, 31, 33, 39, 43
to Functions
 Emphasis on function notation
 Find the domain and range of a relation
 Determine whether a relation is a function
 Evaluate a function
Graphs of
8.2
Full coverage
1-45
Functions
 Use the vertical line test to identify functions
 Obtain information about a function from its
graph
 Review interval notation
 Identify the domain and range of a function
from its graph
The Algebra
8.3
Full coverage
1-57 odd
of Functions
 Find the domain of a function
 Use the algebra of functions to combine
functions and determine domains
Composite
8.4
Full coverage
1-53 odd
and Inverse
 Form composite functions
Functions
 Verify inverse functions
 Find the inverse of a function
 Use the horizontal line test to determine if a
function has an inverse function
 Use the graph of a one-to-one function to
graph its inverse function
Reviewing
9.1
Full coverage
1-35 odd
Linear
 Review how to solve linear inequalities
Inequalities
 Use linear inequalities to solve problems
and Using
involving revenue, cost, and profit
Inequalities
in Business
Applications
Compound
9.2
Full coverage (Emphasis on “and” vs. “or”
1-57 odd
Inequalities
 Find the intersection of two sets
 Solve compound inequalities involving and
 Find the union of two sets
 Solve compound inequalities involving or
Equations and 9.3
Inequalities
Involving
Absolute
Full coverage
 Solve absolute value equations
 Solve absolute value inequalities in the form
1-81 odd
u c

Solve absolute value inequalities in the form
u c
Recognize absolute value inequalities with no
solution or all real numbers as solutions
Full coverage/ Emphasis on function notation and
domain restrictions
 Evaluate square roots and square root
functions
 Find the domain of square root functions
 Simplify expressions of the form n a n
 Find even and odd roots
Full coverage

Radical
Expressions
and Functions
10.1
Rational
Exponents
10.2


10.3
Adding,
Subtracting,
and Dividing
Radical
Expressions
10.4
Multiplying
10.5
With More
Than One
Term and
Rationalizing
Denominators
Radical
Equations
Complex
Numbers
10.6
10.7
1-111 odd
1
n
Use the definition of a
m
n

m
Use the definition of a n
Simplify expressions with rational exponents
Simplify radical expressions using rational
exponents
Full coverage (Emphasis on function notation)
 Use the product rule to multiply radicals
 Use factoring and the product rule to simplify
radicals
 Multiply radicals and then simplify
Full coverage
 Add and subtract radical expressions
 Use the quotient rule to simplify radical
expressions
 Use the quotient rule to divide radical
expressions
Full coverage
 Multiply radical expressions with more than
one term
 Use polynomial special products to multiply
radicals
 Rationalize denominators containing one
term
 Rationalize denominators containing two
terms
Full coverage (Emphasis on function notation)
 Solve radical equations
Full coverage
 Express square roots of negative numbers in
terms of i
 Add and subtract complex numbers



Multiplying
and
Simplifying
Radical
Expressions
Use the definition of a
1-89 odd, 113
1-81 odd
1-65 odd
1-91 odd
1-37 odd
1-99 odd
The Square
Root Property
and
Completing
the Square;
Distance and
Midpoint
Formulas
11.1
The Quadratic
Formula
11.2
Quadratic
Functions and
their Graphs
11.3
 Multiply complex numbers
 Divide complex numbers
 Simplify powers of i
Full coverage
 Solve quadratic equations using the square
root property (Emphasize)
 Complete the square of a binomial
 Solve quadratic equations by completing the
square
 Solve problems using the square root
property
 Find the distance between two points
 Find the midpoint of a line segment
Full coverage
 Solve quadratic equations using the quadratic
formula (Emphasize)
 Use the discriminant to determine the
number and type of solutions
 Determine the most efficient method to use
when solving a quadratic equation
 Write quadratic equations from solutions
 Use the quadratic formula to solve problems
Full coverage/Emphasis on the connection
between vertex form and general form and
connection between graphs and function
notation
 Recognize characteristics of parabolas
 Graph parabolas in the form
1-91
1-57 odd, 77
1-43 odd, 57, 59, 61, 63
2
f  x  a  x  h  k

Graph parabolas in the form
f  x   ax 2  bx  c
Determine a quadratic function's minimum or
maximum value
 Solve problems involving a quadratic
function's minimum or maximum value
Full coverage
 Solve equations that are quadratic in form

Equations
Quadratic in
Form
Exponential
Functions
11.4
Logarithmic
Functions
12.2
12.1
Full coverage
 Evaluate exponential functions
 Graph exponential functions
 Evaluate functions with base e
 Use compound interest formulas
Full coverage (Emphasize the link between
exponential and logarithmic form)
 Change from logarithmic to exponential form
 Change from exponential to logarithmic form
 Evaluate logarithms
 Use basic logarithm properties
 Graph logarithmic functions
1-37
1-47 odd
1-71 odd
Properties of
Logarithms
12.3
Exponential
and
Logarithmic
Equations
12.4
Exponential
Growth and
Decay
12.5
The Circle
13.1
Systems of
13.5
Nonlinear
Equations in
Two Variables
 Find the domain of a logarithmic function
 Use common logarithms
 Use natural logarithms
Full coverage
 Use the product rule
 Use the quotient rule
 Use the power rule
 Expand logarithmic expressions
 Condense logarithmic expressions
 Use the change-of-base property
Full coverage (Emphasize that a logarithm is an
exponent)
 Use like bases to solve exponential equations
 Use logarithms to solve exponential
equations
 Use exponential form to solve logarithmic
equations
 Use the one-to-one property of logarithms to
solve logarithmic equations
 Solve applied problems involving exponential
and logarithmic equations
Full coverage
 Model Exponential Growth and Decay
 Choose an appropriate Model for Data
Full coverage
 Write the standard form of a circle’s equation
 Give the center and radius of a circle whose
equation is in standard form
 Convert the general form of a circle’s
equation to standard form (use completing
the square)
Emphasize systems that include linear and
quadratic equations, and equations of circles.
 Recognize systems of nonlinear equations in
two variables
 Solve systems of nonlinear equations by
substitution
 Solve systems of nonlinear equations by
addition
1-67 odd, 75-85 odd, 80 (answer
is false)
1-89 odd, 99, 111
1-31 odd
1-25 odd
1-8, 11-12, 17-18, 25-28, 30, 3537, 39-42