Test #3 Review Math 1414
I?1
Name Be;
In order to receive full credit you need to show all work.
Solve the equation by expressing each side as a power of
the same base and then equating exponents.
1)4(1+2><)ns4
mm 3
4+
13:
4.)c,>;:127><1
1.
2 a
(a) =
Test #2 Review Math 1414 171
Name 1; g!
a
In order to receive full credit you need to show all work. 3) f(x) _ x4 _ 4x3 + 4x2 =' KWX " lYail'q')
l
y 7" X cfw_1'40
Complete the following:
(3) Leading Coefficient, Degree, 8: the end behavior.
(b) Find the
Test #1 Review Math 1414
171
Name Kg T/ _ _
In order to receive full credit you need to show all work.
Simplify.
1) 22  32+3(42 12)2+2
: 2a3+3(bra)1.;.g
= 22 5+5(4)3;z
=32q+3UM2
=32 CI~t48:9.
:22 0: +2Lt
= 15 Ht
Eil
Solve the equation. LCD: l3
2) 7
Fraction to Decimal Conversion Table
fraction  decimal I
in
 E
 a:
Oilh
= 0.8
bu'hu
MIA gala U'IIl NA w_\ Mg AH
II
p o o p c o 
N
01
tD~l DIN 0qu NIUI NIN GIUI UIIN hlw WIN
II
o o p o p o o o o
N
00 
01
\l
A
h
= 428
EVEN FUNCTIONS:

Exponents are even
End behavior is the same for the
left and the right
Negative leading coefficient will
switch the end behavior
a>0
a<0
EVEN ROOTS:

Multiplicity is even
Graph will bounce at zero
ODD FUNCTIONS:

Exponents are odd
End
Graph of Polynomial Function:
Function:
2) Find xintercepts:
1) Degree:
3) Find yintercepts:
5) Determine the number of turning points:
4) Determine multiplicity/behavior of xintercepts:
6) Determine end behavior:
7) Create table of points:
8) Graph fun
Fractions
A fraction is a part of a whole
Slice a pizza, and you will have fractions:
1
1
/2
(OneHalf)
3
/4
(OneQuarter)
/8
(ThreeEighths)
The top number tells how many slices you have
The bottom number tells how many slices the pizza
wascut into.
Equi
Translating Word Problems
Word List:
Addition
Add
Sum
*More than
Total
Increased by
Subtraction
Subtract
Difference
Less
*Less than
Decreased by
Minus
*Subtracted from
Exponent(Power)
Squared (2nd power)
Cubed (3rd power)
Fourth power (4th power)
Multipli
Greatest Common Factor
The highest number that divides exactly into two or more numbers.
It is the "greatest" thing for simplifying fractions!
Let's start with an Example .
Greatest Common Factor of 12
and 16
Find all the Factors of each
number,
Circle th
Adding Fractions with Different Denominators
But what if the denominators (the bottom numbers) are not the same? As in
this example:
3
/8
+
1
/4
+
=
?
=
You must somehow make the denominators the same.
In this case it is easy, because we know that 1/4 is
538 I Chapter 6 Systems of Equations
El
" PR DJ E 0 T5
1. FINDING ZEROS OF A POLYNOMIAL One zero of c. What is the slope of the line betweenO and P?
P(x) = x3 + 2x2 + Cx 6 is the sum of the other two . , . _ .
zeros of Pa). Find C and the three zeros of
Conic Sections
Standard Forms of the Equation of a Parabola
Equation
Vertex
Focus
Directrix
Axis of Symmetry
Opens
x 2 = 4 py y 2 = 4 px ( x  h) 2 = 4 p ( y  k ) ( y  k ) 2 = 4 p ( x  h)
(0, 0) (0, 0) (h, k )
(0, p) ( p, 0) (h, k + p )
Name_
6.1: Conic Sections
PARABOLA
A parabola is the set of points in the plane that are equidistant from a fixed line (the directrix) and a fixed point (the focus) not on the directrix.
The midpoint of the line segment between the focus and the d
Name_
3.6: Exponential Growth and Decay
The Compound Interest Formula nt A = P 1 + r n
where
A = balance P = principal r = interest rate (expressed as a decimal) t = time n = the number of times compounded
Continuous Compounding Interest Formula
Name_
3.5: Exponential and Logarithmic Equations
SOLVE EXPONENTIAL EQUATIONS
Equality of Exponents Theorem
x y If b = b , then x = y, provided that b > 0 and b 1.
Example: Solve for x algebraically.
3
x  2
= 81
Solution:
3
x  2 x
Name_
3.4: Logarithms and Logarithmic Scales
Properties of Logarithms In the following properties, b, M, and N are positive real numbers (b 1). Product Property logb (MN) = logb M + logb N Quoti
Name_
3.3: Logarithmic Functions
If x > 0 and b is a positive constant (b 1), then y = logb x if and only if by = x.
The exponential form of y = logb x is by = x. The logarithmic form of by =
Name_
3.2: Exponential Functions
The exponential function with base b is defined by f(x) = bx where b > 0, b 1, and x is a real number. 1. Evaluate f(x) = 3 x at x = 4, x = 3, a
3.3: Zeros of Polynomial Functions
A polynomial function P of degree n has at most n zeros, where each zero of multiplicity k is counted k times.
The Rational Zero Theorem
If P(x) = anx n + an1x n1 + . . . + a1x + a0 has integer coefficients (an 0
2.5  Transformations of Graphs
Every College Algebra student must be able to identify the following six parent graphs.
f(x) = x
y
f(x) = x2
y
x
x
Domain = _ Range = _
Domain = __ Range = _
f(x) = x
3
y
f(x) = x
y
x
x
Domain = _ Range =
3.1: The Remainder Theorem and Factor Theorem
Consider the polynomial function P(x)
= x3  7x  6. Notice,
P(1) = (1)3  7(1)  6 = 1 + 7  6 =0
So, 1 is called a zero of the function P. We will be interested in finding the zeros of many polyn
Steps To Graph Rational Functions
1. Make sure the numerator and denominator of the function are arranged in the correct descending order of power. 2. Find the Domain a. Factor the denominator of the function completely. b. Find the real zeros of the
Steps To Graph Polynomial Functions
1. Make sure the function is arranged in the correct descending order of power.
f(x) = anx + an1x
n
n1
+ . . . + a1x + a0 , where the leading coefficient an 0
2. Determine the farleft and farright behavio
2.4  Graphing Quadratic Functions
A quadratic function of x is of the form
f(x) = ax2 + bx + c
where a, b, and c are real numbers and a 0. This equation is called the expanded form of the function, and its graph is called a parabola.
y axis of sym
3.2: Polynomial Functions of Higher Degree
So far, we have only graphed two kinds of polynomial functions this semester: lines and parabolas. In this section we will graph polynomials of degree 3 or higher. All polynomial functions have graphs that a
2.3  Linear Functions
Definition of a Linear Function A linear function of x is of the form
f(x) = mx + b, m 0
where m and b are real numbers.
The slope of the line is the steepness, or rate of change between any two points on the line.
y y2 P2