College Algebra
Fall 2005
Quiz No. 9
1. Graph the following system of inequalities and clearly label the coordinates of each of the vertices.
yx1
y
yx3
2x5
x
2. Marita will take a test that has questions in group A worth 9 points each and questions in gro
College Algebra Case Studies
Polynomial Inequalities
Business Application
Big Kids Toy Co. performed an analysis of the profits and losses from two of their divisions, the
gaming and the stuffed toy divisions. They developed models that approximately desc
College Algebra Review
In-Class Worksheet
A. Add or subtract and, if possible, simplify:
1.
5
3
4z 8z
2.
2
y
y y 20 y + 4
3.
3y
2y
2
y 7 y + 10 y 8 y + 15
4.
6a
3b
5
+ 2
a b b + a a b2
5.
x +8
7
3x 2
+
2
x+2 4x
4 4x + x 2
2
2
B. Simplify the following co
Application 1
A large electronics firm finds that the number of computers it can produce per week after t
weeks of production is approximated by
C( t ) =
2000 t 2 + 20 ,000 t
, t 50
t 2 + 10 t + 25
(a)
How many computers did it produce the first week?
(b)
Inverse Functions (Section 4.1)
We say f -1(x) is inverse of f(x) if f -1(f(x) = x.
-1
-1
If f (f(x) = x, then we also have f(f (x) = x.
Our text expresses this as f -1(x) being the inverse of f(x).
So, f -1(f(x)=x and f(f -1(x)=x.
Some texts write f -1(f
Exponential Functions
(The Mathematics of God?)
The things that you have heard from me in the presence of
many witnesses, these entrust to faithful men who will be
able teach others also.
II Timothy 2:2
me
(Paul)
you
(Timothy)
20 = 1
faithful men
others
2
Finding Zeros of a Polynomial
Given polynomial P(x), we want to find where P(x) = 0
Example: Find zeros of P(x) = 2x3 + 9x2 2x 9
In other words, we want the x that satisfies:
2x3 + 9x2 2x 9 = 0
Graphically, this is when P(x) crosses the x-axis
60
P(x) = 2
Division of Polynomials and Zeros of a Polynomial
Start with
10
g(x) = x2 - 2x 8
g (x ) = x 2- 2x - 8
= (x + 2)(x 4)
5
To find zeros we solve for g(x) = 0
g(x) = x2 - 2x 8
0
-5
-4
-3
-2
-1
0
1
2
3
4
5
= (x + 2)(x 4)
= 0
if x = -2 or x = 4
That is g(-2) =
Exponential Functions and Their Graphs (Section 4.2)
1. Graph and label each exponential function on the grid given below. Answer the questions for each
function by inspecting your graph and from what we discussed in class.
x
(a) f ( x) = 2
1
x
(b) g ( x)
Simplifying a Rational Expression
3 x 2 20 x 7 ( x 7)(3 x + 1) 3 x + 1
=
=
2
( x 7)(2 x + 3) 2 x + 3
2 x 11x 21
Domain cfw_x: x=all real nos. except 7 and -3/2
Simplifying a Rational Expression When Dividing
x 2 + 9 x + 18 x 2 + 6 x + 9
2
2
x 36
x 2 x 24