REVIEW OF ALGEBRA
Business Math 2
1-Measurement Formulas and Monomials
2-Multiplying and Dividing Monomials
3-Adding and Subtracting Polynomials
4-Multiplying Monomials and Polynomials
5-Multiplying Polynomials
6-Factoring Trinomials of the Form x2+bx+c
7
BUSINESS MATH 2
Review of Algebra
1
The Real Number Line
The Real Number Line is a pictorial
representation of Real Numbers. A real number
can be thought of as a number that can be
represented on the Real number line.
a>0
b<0
b
a>b
0
if and only if
a
ab>0
Limits and Continuity
Definition
Evaluation of Limits
Continuity
Limits Involving Infinity
Limit
We say that the limit of f ( x) as x approaches a is L and write
lim f ( x) L
x a
if the values of f ( x) approach L as x approaches a.
y f ( x)
L
a
Limits, G
Parallel and Perpendicular Lines
y mx b
From
Intermediate
Algebra
Slope-Intercept Form
Useful for graphing since m is the slope and b is the y-intercept
y y1 m x x1
Point-Slope Form
Use this form when you know a point on the line and the slope
Also can u
INVERSE
FUNCTIONS
Remember we talked about functions-taking a
set X and mapping into a Set Y
11
22
33
44
55
Set X
22
44
66
88
10
10
Set Y
An inverse function would reverse that process
and map from SetY back into Set X
If we map what we get out of the fun
Limits,
Continuity and
the Derivative
1
The Derivative and the Slope of a Graph
Consider the case of an object moving along a curve
from left to right.
At the point where the
object is released, it
continues in a straight
line. This line is called the
tan
Lets examine exponential functions. They are
different than any of the other types of functions weve
studied because the independent variable is in the
exponent.
x
3
2
1
0
-1
-2
-3
2x
8
4
2
1
1/2
1/4
1/8
f x 2
Lets look at the graph of
this function by pl
MARGINAL ANALYSIS
ENTREP 411
BUSINESS MATHEMATICS 2
EXAMPLES
C (x)
1. Suppose that dollars is the total cost of
C ( x) 110 x 0.02 x
manufacturing x4toys and
. Find
a. the marginal cost function
b. the marginal cost when x = 50
c. the actual cost of manufa
ENTREP 411
BUSINESS MATHEMATICS 2
REVIEWER
FOURTH LONG EXAM
I.
MULTIPLE CHOICE
II.
TRUE OR FALSE
III.
PROBLEM SOLVING
1. Evaluate the following limits:
a.
(answer: 7)
lim( x 2 2 x 1)
x 2
b.
lim( x 3 2 x 2 3 x 4)
(answer: -10)
x 1
c.
d.
x 2 3x 4
lim 2
x
Exponential & Logarithmic
Functions
Table of Contents
Exponential Functions
Logarithmic Functions
Converting between Exponents and
Logarithms
Properties of Logarithms
Exponential and Logarithmic Equations
General Form of Exponential
Function
Domain: All
r
Growth
Decay
Exponential function A function of the form y=abx,
where b>0 and b1.
Step 1 Make a table of values for the function.
x
y 3
x
2
3
0
2
3
3
2
0
2
3
3
3
y
1
y 3
x
1
9
2
1
9
27
3
Now that you have a data table of ordered pairs for the
function, yo
Remember integers are 2, -1, 0, 1, 2 (no decimals
or fractions) so positive integers would be 0, 1, 2
A polynomial function is a function of the form:
n must be a positive integer
f x an x an 1 x
n
n 1
a1 x ao
All of these coefficients are real numbers
Relations
And
Functions
A relation is a set of ordered pairs.
The domain is the set of all x values in the relation
domain = cfw_-1,0,2,4,9
These are the x values written in a set from smallest to largest
cfw_(2,3), (-1,5), (4,-2), (9,9), (0,-6)
These are
RATIONAL
FUNCTIONS
A rational function is a function of the form:
p x
R x
q x
where p and q are
polynomials
p x
R x
q x
What would the domain of a
rational function be?
Wed need to make sure the
denominator 0
2
5x
R x
3 x
x : x 3
Find the domain.
Graphs of Rational Functions
BUSINESS MATH 2
A rational function is a function that can be expressed in the form
f ( x)
y
g ( x)
where both f(x) and g(x) are polynomial functions.
Examples of rational functions would be:
1
y
x 2
2x
f ( x)
3 x
x2 4
g ( x)
ENTREP 411 BUSINESS MATH 2
MIDTERM EXAM REVIEWER
SECOND SEMESTER 2012-2013
I.
MULTIPLE CHOICE. Write the letter corresponding to the correct answer. Write N if none of the given
choices is correct. (2 poin
The sum f + g
f g x f x g x
This just says that to find the sum of two functions, add
them together. You should simplify by finding like terms.
f x 2 x 3
g x 4 x 1
2
3
2
3
f g 2 x 3 4 x 1
3
2
4 x 2 x 4
Combine like
terms & put in
descending
order
The di
gin
ri
O
Cartesian Coordinate
System
X Axis
Y Axis
s
Ordered Pair
Coordinates
Terminologies:
Cartesian Coordinate
plane
a two-dimensional surface
on which a coordinate system
has been set up; invented by
Rene Descartes; also called
Cartesian
plane,
graph,
The Distance and Midpoint
Formulas
Goal 1
Goal 2
two
Goal 3
Find the Midpoint of a
Segment
Find the distance between
points on a coordinate plane
Find the slope of a line between two
points on a coordinate plane
Distance Formula
Used to find the distance
The standard form of the equation of a circle with
its center at the origin is
2
2
2
x y r
r is the radius of the circle so if we take the square root of the
right hand side, we'll know how big the radius is.
Notice that both the x and y terms are squared
6/21/2012
Business Math
1 - Whole Numbers
1,605,743,891,412
1
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2
6/21/2012
How to Dissect and Solve a Word Problem
Given
Unknowns
Formulas
Reinforcements
3
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4
6/21/2012
2 - Fractions
5
6/21/2012
Types of Fractions
6
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7
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