Graphing Rational Functions
9.1
Rational Function an equation in the form f ( x)
p ( x)
where p(x) and g(x) are polynomial functions.
g ( x)
Example 1
Example 2
x -1
Graph f ( x)
3
Graph f ( x)
x
Example 3
x( x - 3)
Example 4
2
x -9
Graph f ( x)
x+3
(x
Ex
Distance and Midpoint Formula
7.1
Distance Formula
d
( x2 - x1 )
2
( y 2 - y1 )
2
Example 1
Find the distance between the points (4, 4) and (-6, -2).
Example 2
Find the value of a to make the distance = 10 units given the points
(-7, 3) and (a, 11).
Examp
Solving Quadratic Equations by Graphing
6.1
Quadratic Function
f ( x) = ax 2 + bx + c
Write each in quadratic form.
Example 1
f ( x) = 3(x + 2)2
Example 2
Graph f ( x) = x 2 + 6x + 8
Example 3
An arrow is shot upward with an initial velocity of 64 ft / se
Monomials
5.1
Express each in Scientific Notation
Example 1
236,000
Example 2
.001084
Monomial an algebraic expression that is a number, variable, or the product of a number and one or
more variables.
ex. 12x, -8, 16a 2b3c
Constant (No Variables)
4, -9
Co
The Counting Principle
12.1
Solve problems by using the fundamental counting principle
Solve problems by using the strategy of solving a simpler problem
Dependent Events
Independent Events
Fundamental counting principle
Example 1
How many three-letter pat
Relations and Functions
2.1
4
A
B
2
D
-5
5
C
E
-2
F
-4
Relation a set of ordered pairs (Domain, Range).
Mapping shows how each number of the domain is paired with each member of the range.
Example 1
(2, 4), (3, 0), (5, -2), (6, 0)
Function a special type
Real Exponents and Exponential Functions
10.1
Simplify expressions and solve equations involving real exponents
Exponential function
Exponential Function an equation of the form y = a b x where
a 0, b > 0, and b 1, is called an exponential function with b
Polynomial Functions
8.1
Polynomial in One Variable
a0 xn + a1xn 1 + a2 xn 2 + .an 1x + an
a0 , a1 , ., an - real numbers
Descending order
n must be a nonnegative integer
One variable.
Example 1
Determine if each expression is a polynomial in one variable
An Introduction to Trigonometry
13.1
Trig Identities
sin
opposite
cos
hypotenuse
csc
hypotenuse
adjacent
tan
adjacent
hypotenuse
sec
opposite
opposite
hypotenuse
cot
adjacent
adjacent
opposite
Example 1
Find the six trig functions for angle .
3 5
3
Solving Systems of Equations by Graphing
3.1
Systems of Equations a set of equations with the same variables.
Consistent System a system that has at least one solution.
Inconsistent System a system that does not have a solution.
Independent System a syste
An Introduction to Matrices
4.1
columns
2 3 5 6
C = 4 8 7 2 rows
1 0 5 9
Each value is called an Element
C3 x 4
Matrix Logic
Example 1
Jim, Mario, and Mike are married to Shana,
Kelly and Lisa. Use these clues to find out
who is married to whom.
1. Mario