M2ng_nt.08
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8.7
Modeling with Exponential
and Power Functions
Goals p Model data with exponential functions.
p Model data with power functions.
Your Notes
Writing an Exponential Function
Example 1
Write an exponential function y
t

2.7
Piecewise Functions
Goals p Represent piecewise functions.
p Use piecewise functions to model real-life quantities.
Your Notes
VOCABULARY
Piecewise function A function represented by a
combination of equations, each corresponding to a
part of the doma

2.4
Writing Equations of Lines
Goals p Write linear equations.
p Write direct variation equations.
Your Notes
VOCABULARY
Direct variation Two variables x and y show direct
variation provided y kx where k is a nonzero
constant.
Constant of variation The no

2.1
Functions and Their Graphs
Goals p Represent relations and functions.
p Graph and evaluate linear functions.
Your Notes
VOCABULARY
Relation A pairing of input values with output values
Domain of a relation The set of input values for a
relation
Range

4.2
Multiplying Matrices
Goals p Multiply two matrices.
p Use matrix multiplication in real-life situations.
Your Notes
Describing Matrix Products
Example 1
State whether the product AB is defined. If so, give the
dimensions of AB.
a. A: 3
4, B: 2
4
b. A:

4.3
Determinants and Cramers Rule
Goals p Evaluate determinants.
p Use Cramers Rule.
Your Notes
VOCABULARY
Determinant A real number associated with any square
matrix A, denoted by det A or by A
Cramers rule A method for solving a system of linear
equatio

7.6
Solving Radical Equations
Goals p Solve equations that contain radicals.
p Use radical equations to solve real-life problems.
Your Notes
VOCABULARY
Extraneous solution A solution of a transformed
equation that is not a valid solution of the original
e

4.1
Matrix Operations
Goals p Add and subtract matrices, multiply a matrix by a
scalar, and solve matrix equations.
p Use matrices in real-life situations.
Your Notes
VOCABULARY
Matrix A rectangular arrangement of numbers in rows
and columns
Dimensions of

4.4
Identity and Inverse Matrices
Goals p Find and use inverse matrices.
p Use inverse matrices in real-life situations.
Your Notes
VOCABULARY
Identity matrix An n n matrix that has 1s on the main
diagonal and 0s elsewhere
Inverse matrices Two n n matrice

2.8
Absolute Value Functions
Goals p Represent absolute value functions.
p Use absolute value functions to model real-life
situations.
Your Notes
VOCABULARY
Vertex of an absolute value graph The corner point of the
graph of an absolute value function
GRAP

4.5
Solving Systems
Using Inverse Matrices
Goals p Solve systems using inverse matrices.
p Use systems to solve real-life problems.
Your Notes
VOCABULARY
Matrix of variables The matrix of variables of the linear
x
ax by e
system
is y .
cx dy f
Matrix of c

7.3
Power Functions and
Function Operations
Goals p Perform operations with functions.
p Use function operations to solve real-life problems.
Your Notes
VOCABULARY
Power function A function of the form y ax b where a
is a real number and b is a rational n

7.4
Inverse Functions
Goals p Find inverses of linear functions.
p Find inverses of nonlinear functions.
Your Notes
VOCABULARY
Inverse relation A relation that maps the output values
of an original relation back to their original input
values
Inverse func

7.2
Properties of Rational Exponents
Goals p Use properties of rational exponents.
p Use properties of rational exponents in real life.
Your Notes
VOCABULARY
Simplest form of a radical A radical expression after you
apply the properties of radicals, remov

7.1
n th Roots and Rational
Exponents
Goals p Evaluate n th roots using radical notation and rational
exponent notation.
p Use n th roots to solve real-life problems.
Your Notes
VOCABULARY
nth root of a For an integer n greater than 1, if bn
then b is an

7.5
Graphing Square Root
and Cube Root Functions
Goals p Graph square root and cube root functions.
p Use radical functions to find real-life quantities.
Your Notes
VOCABULARY
Radical function A function containing a radical such as
x
y
GRAPHS OF RADICAL

8.6
Solving Exponential and
Logarithmic Equations
Goals p Solve exponential equations.
p Solve logarithmic equations.
Your Notes
Example 1
Solving by Equating Exponents
Solve 272x
9x
Solution
272x 9 x
( 33 )2x
2.
2
Write original equation.
( 32 ) x
2
Rewr

8.5
Properties of Logarithms
Goals p Use properties of logarithms.
p Use properties of logarithms to solve real-life
problems.
Your Notes
PROPERTIES OF LOGARITHMS
Let b, u, and v be positive numbers such that b
Product Property
Quotient Property
Power Pro

8.2
Exponential Decay
Goals p Graph exponential decay functions.
p Use exponential decay functions to model real-life
situations.
Your Notes
VOCABULARY
Exponential decay function A function of the form
f (x) ab x where a > 0 and 0 < b < 1
Decay factor The

8.1
Exponential Growth
Goals p Graph exponential growth functions.
p Use exponential growth models.
Your Notes
VOCABULARY
Exponential function A function that involves the
expression bx where the base b is a positive number
other than 1
Asymptote A line t

8.3
The Number e
Goals p Use e as the base of exponential functions.
p Use the natural base e in real-life situations.
Your Notes
THE NATURAL BASE e
The natural base e is irrational. It is defined as follows:
1n
As n approaches
,1
approaches
n
e 2.7182818

8.4
Logarithmic Functions
Goals p Evaluate logarithmic functions.
p Graph logarithmic functions.
Your Notes
VOCABULARY
Common logarithm The logarithm with base 10
Natural logarithm The logarithm with base e
DEFINITION OF LOGARITHM WITH BASE b
Let b and y

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