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Index Index

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