# Intermediate Algebra: Functions and Graphs

## IndexIndex

a$$\vphantom{a}^{m/n}$$. See rational exponents
absolute value
equations
inequalities
acid (pH) scale
algebraic equation, Item
algebraic fraction
dividing
multiplying
reducing
allometric equations
ascending powers
astronomical units
asymptote
horizontal
of hyperbola
vertical
axis
conjugate
major
minor
of symmetry, Item
transverse
back-substitution
base
of a logarithm
of an exponential function
base 10 logarithms. See common logarithms
binomial, Note
cube of
opposite of
special products of
square of
branches. See hyperbola
break even
building factor
Bézier curves
carrying capacity
center
of a circle
of an ellipse
of hyperbola
central
conics
ellipse
hyperbola
central conic
central rectangle
change in. See Delta
circle
center
equation of
common logarithms
completing the square
complex fraction
simplify
complex number
compound inequality
compound interest
balance
principal
compounded continuously
concave down
concave up
conic. See conic section
conic section, Paragraph Paragraph Paragraph Paragraph Assemblage. See also circle, ellipse, hyperbola, parabola
central
degenerate
standard form
systems involving
conjugate
pair
consistent. See system of equations
constant of variation
continuous compounding, Item
conversion equations
coordinate formula for slope
cost
covertices. See ellipse
cross-multiplying. See proportion
cube of a binomial
cube root
cubic formula
cubic spline
curve fitting
decay factor
decibel scale
decreasing function
degenerate conic
degree (of a polynomial)
of a product
Delta ($$\Delta$$), Example. See also net change
demand equation
dependent, Item
dependent system. See system of equations
descending powers
direct variation
constant of variation
finding a formula for
scaling exponent
scaling property
test for
with a power
discriminant
distance
(absolute value)
formula
distance formula
dividing algebraic fractions
doubling time
e$$\thinspace$$
central
covertices
finding the equation of
foci
major axis
minor axis
standard form
translated
vertices
empirical model
equation
algebraic, Item
allometric
demand
first-degree
graphical solution
in two variables
supply
with fractions
equilibrium price
evaluating the function
exponent
(logarithm)
integer
laws of
negative
scaling
zero
exponential decay
decay factor
exponential equation
graphical solution of
solving
solving with logarithms
exponential function
base of
finding a formula
natural
vs linear growth
vs power functions
exponential growth
growth factor
initial value
vs linear growth
vs power function
exponential growth and decay
exponential notation
extraneous solution
extrapolation
factor
factoring, Note
cubics
first-degree equation
focus
of a hyperbola
of an ellipse
fraction
building factor
common factor
complex
dividing
fundamental principal
lowest common denominator (see lowest common denominator)
multiplying
reducing
reducing an algebraic fraction
simplify
unlike
function
absolute value (see absolute value)
direct variation
exponential
exponential growth and decay
input variable
inverse variation
natural exponential
notation
output variable
polynomial
rational
vertical line test
fundamental principal of fractions
general form for a linear equation
of a circle
geometric formulas
golden rectangle
graph
concave down
concave up
concavity
eight basic
graphing an inequality using a test point
increasing
growth by a constant percent
half-life
half-plane
horizontal asymptote
horizontal line
slope of
hyperbola
asymptotes
branches
central
conjugate axis
translated
transverse axis
vertices
i$$\thinspace$$
imaginary number
imaginary unit. See i$$\thinspace$$
inconsistent, Item
inconsistent system. See system of equations
increasing graph
independent system. See system of equations
inequality, Note
compound
graphical solution
linear
strict
system of
infinity ($$\infty$$)
initial value
input variable. See function
intercept method of graphing
interpolation
intersect
interval notation
closed interval, Item
half closed, Item
half open, Item
infinite interval
open interval, Item
inverse square law
inverse variation
test for
with a power
irrational numbers
Kleiber’s Rule
laws of exponents
LCD. See lowest common denominator
least-squares regression line
like fractions
line
horizontal
of best fit (see least-squares regression line)
parallel
perpendicular
regression
vertical
linear equation
general form
graph using the intercept method
point-slope formula
slope-intercept form
linear growth
linear inequality
linear regression
extrapolation
interpolation
least-squares regression line
line of best fit
outliers, Item
$$2\times 2$$
$$3\times 3$$
log-log graph paper
logarithm
base
conversion equations
equation
properties
scale
some useful
logarithmic function
logarithms
common (base 10)
lowest common denominator
clearing fractions with
finding the
lowest common multiple (LCM)
major axis. See ellipse
mathematical model
mechanistic models
midpoint
minor axis. See ellipse
model
empirical
mechanistic
Moore’s law
muliplying algebraic fractions
multiplicity
n$$\vphantom{n}^{\text{th}}$$ root
natural base, Section Paragraph Item. See also e$$\thinspace$$
natural exponential function
natural log function
natural logarithm
negative and zero exponents
negative exponents
negative reciprocal
net change
opposite of a binomial
ordered triple
output variable. See function
parabola
axis of symmetry, Item
maximum value, Note
minimum value, Note
vertex form
vertex of
parallel lines
percent decrease
percent increase
perfect square
perpendicular lines
pH scale
point-slope formula
polynomial
ascending powers
descending powers
division
function
modeling with
products of
positive root. See principal root
power function
vs exponential function
vs exponential functions
principal
product of fractions
profit
properties of exponential functions
property of proportions
proportion
cross-multiplying
proportional
directly
find using three points
graph of
maximum value, Note
minimum value, Note
multiplicity
parameters
solutions of
solve by factoring
solving by completing the square
solving by extraction of roots
solving by graphing
vertex form
algebraic solution
graphical solution
quotient of fractions
exponential notation
quotient rule for
rationalizing the denominator
simpifying
sums and differences of
rate
ratio method
rational exponents
rational function
reducing fractions
regression. See linear regression
revenue
Richter scale (or magnitude)
root
cube root
n$$\vphantom{n}^{\text{th}}$$
of negative numbers
of powers
of real numbers
principal root
square root
scaling exponent
scaling property of direct variation
scatterplot, Item
scientific notation
simplifying a complex fraction
coordinate formula for
of a line
positive
rate of change
undefined
zero
slope-intercept form
slope-intercept formula. See slope-intercept form
solution
to a system of equations
to an equation in one variable
to an equation in two variables
to an inequality in one variable
to system of equations
special products of binomials
square root
starting value. See initial value
strict inequality
substitution method. See system of equations
sum or difference of fractions
supply equation
surface area
of a cone
of a cylinder
of a pyramid
of a sphere
symmetry. See axis of symmetry
system of equations. See system of equations
$$2\times 2$$
$$3\times 3$$
back-subsitution
consistent and independent
dependent
elimination method
Gaussian reduction
graphing
inconsistent
independent
involving conic sections
linear combination
solution
substitution method
system of inequalities
table of values, Item
test for direct variation
test for inverse variation
test point for inequalities
transverse axis. See hyperbola
triangular form
variation. See direct variation; inverse variation
varies directly
varies inversely
vertex
of a hyperbola
of a parabola
of a system of inequalities
of ellipse
vertex form
for a parabola
vertex of a parabola
vertical asymptote
vertical line
slope of
vertical line test. See function
vertices. See ellipse; hyperbola; system of inequalities
volume
of a cone
of a cylinder
of a pyramid
of a sphere
World3
x-intercept
y-intercept
zero exponent
zero-factor principle