Modeling with Exponential
and Power Functions
Goals p Model data with exponential functions.
p Model data with power functions.
Writing an Exponential Function
Write an exponential function y
Goals p Represent piecewise functions.
p Use piecewise functions to model real-life quantities.
Piecewise function A function represented by a
combination of equations, each corresponding to a
part of the doma
Writing Equations of Lines
Goals p Write linear equations.
p Write direct variation equations.
Direct variation Two variables x and y show direct
variation provided y kx where k is a nonzero
Constant of variation The no
Functions and Their Graphs
Goals p Represent relations and functions.
p Graph and evaluate linear functions.
Relation A pairing of input values with output values
Domain of a relation The set of input values for a
Goals p Multiply two matrices.
p Use matrix multiplication in real-life situations.
Describing Matrix Products
State whether the product AB is defined. If so, give the
dimensions of AB.
a. A: 3
4, B: 2
Determinants and Cramers Rule
Goals p Evaluate determinants.
p Use Cramers Rule.
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
Solving Radical Equations
Goals p Solve equations that contain radicals.
p Use radical equations to solve real-life problems.
Extraneous solution A solution of a transformed
equation that is not a valid solution of the original
Goals p Add and subtract matrices, multiply a matrix by a
scalar, and solve matrix equations.
p Use matrices in real-life situations.
Matrix A rectangular arrangement of numbers in rows
Identity and Inverse Matrices
Goals p Find and use inverse matrices.
p Use inverse matrices in real-life situations.
Identity matrix An n n matrix that has 1s on the main
diagonal and 0s elsewhere
Inverse matrices Two n n matrice
Absolute Value Functions
Goals p Represent absolute value functions.
p Use absolute value functions to model real-life
Vertex of an absolute value graph The corner point of the
graph of an absolute value function
Using Inverse Matrices
Goals p Solve systems using inverse matrices.
p Use systems to solve real-life problems.
Matrix of variables The matrix of variables of the linear
ax by e
is y .
cx dy f
Matrix of c
Power Functions and
Goals p Perform operations with functions.
p Use function operations to solve real-life problems.
Power function A function of the form y ax b where a
is a real number and b is a rational n
Goals p Find inverses of linear functions.
p Find inverses of nonlinear functions.
Inverse relation A relation that maps the output values
of an original relation back to their original input
Properties of Rational Exponents
Goals p Use properties of rational exponents.
p Use properties of rational exponents in real life.
Simplest form of a radical A radical expression after you
apply the properties of radicals, remov
n th Roots and Rational
Goals p Evaluate n th roots using radical notation and rational
p Use n th roots to solve real-life problems.
nth root of a For an integer n greater than 1, if bn
then b is an
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.
Radical function A function containing a radical such as
GRAPHS OF RADICAL
Solving Exponential and
Goals p Solve exponential equations.
p Solve logarithmic equations.
Solving by Equating Exponents
272x 9 x
( 33 )2x
Write original equation.
( 32 ) x
Properties of Logarithms
Goals p Use properties of logarithms.
p Use properties of logarithms to solve real-life
PROPERTIES OF LOGARITHMS
Let b, u, and v be positive numbers such that b
Goals p Graph exponential decay functions.
p Use exponential decay functions to model real-life
Exponential decay function A function of the form
f (x) ab x where a > 0 and 0 < b < 1
Decay factor The
Goals p Graph exponential growth functions.
p Use exponential growth models.
Exponential function A function that involves the
expression bx where the base b is a positive number
other than 1
Asymptote A line t
The Number e
Goals p Use e as the base of exponential functions.
p Use the natural base e in real-life situations.
THE NATURAL BASE e
The natural base e is irrational. It is defined as follows:
As n approaches
Goals p Evaluate logarithmic functions.
p Graph logarithmic functions.
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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