## Index Index

*a*\(\vphantom{a}^{m/n}\).

*See*rational exponents

absolute value, Paragraph Definition

equations, Subsection Assemblage

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

asymptote

of hyperbola, Paragraph

axis

conjugate, Paragraph

major, Paragraph

minor, Paragraph

of symmetry, Item

transverse, Paragraph

axis of symmetry, Item.

*See also*parabolaback-substitution, Subsection Paragraph

balance, Assemblage.

*See also*compound interestbase, Definition Assemblage

of a logarithm, Definition

of an exponential function, Paragraph

base 10 logarithms.

*See*common logarithmsbinomial, Note

cube of, Assemblage

denominator with radical, Paragraph

opposite of, Subsection

special products of, Assemblage

square of, Paragraph

branches.

*See*hyperbolabreak even, Paragraph

building factor, Paragraph

Bézier curves, Paragraph

center

of a circle, Paragraph

of an ellipse, Assemblage Assemblage

of hyperbola, Assemblage Assemblage

central

conics, Subsection

ellipse, Assemblage

hyperbola, Assemblage

central conic, Paragraph

central rectangle, Paragraph

change in.

*See*Deltacenter, Paragraph Assemblage

equation of, Assemblage

general quadratic form, Paragraph

radius, Assemblage

closed interval, Item.

*See also*interval notationcommon factor, Paragraph.

*See also*fractioncommon logarithms, Paragraph

complex conjugate, Assemblage.

*See also*conjugate paircomplex 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 downconic.

*See*conic sectionconic section, Paragraph Paragraph Paragraph Paragraph Assemblage.

*See also*circle, ellipse, hyperbola, parabolacentral, Subsection

degenerate, Paragraph

standard form, Paragraph

systems involving, Subsection

conjugate, Paragraph

pair, Paragraph

conjugate axis, Paragraph.

*See also*hyperbolaconjugate pair, Paragraph.

*See also*complex conjugateconsistent.

*See*system of equationsconstant of variation, Assemblage Assemblage Paragraph

continuous compounding, Item

conversion equations, Assemblage

coordinate formula for slope, Subsection Assemblage

cost, Paragraph

covertices.

*See*ellipsecross-multiplying.

*See*proportioncube of a binomial, Assemblage

cube root, Definition

cubic formula, Paragraph

cubic spline, Paragraph

decibel scale, Paragraph

decreasing graph, Paragraph.

*See also*decreasing functionof a product, Assemblage

Delta (\(\Delta\)), Example.

*See also*net changedemand equation, Paragraph

dependent, Item

dependent system.

*See*system of equationsdescending 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 variationdiscriminant, Paragraph Assemblage

distance

(absolute value), Subsection

formula, Assemblage

distance formula, Paragraph

dividing algebraic fractions, Assemblage

doubling time, Subsection Assemblage

elimination method, Subsection Subsection.

*See also*system of equationscentral, 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

equation

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

negative, Assemblage Caution Subsection

scaling, Paragraph

zero, Assemblage Assemblage

exponential decay, Investigation Paragraph Paragraph Paragraph Assemblage

decay factor, Paragraph

graphical solution of, Subsection

solving, Paragraph Paragraph Assemblage Paragraph

solving with logarithms, Assemblage Subsection Paragraph

exponential function, Definition Assemblage Caution Paragraph Paragraph

base of, Paragraph

finding a formula, Assemblage

natural, Paragraph

vs linear growth, Subsection

vs power functions, Subsection Assemblage

exponential growth, Assemblage Paragraph Paragraph Paragraph Assemblage

growth factor, Paragraph Assemblage Assemblage Item

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 equationextrapolation, Subsection Paragraph

factor, Section

factored form, Paragraph.

*See also*quadratic equationfactoring, Note

cubics, Assemblage

solve a quadratic equation by, Subsection Assemblage

first-degree equation, Paragraph

focus

of a hyperbola, Definition

of an ellipse, Definition

fraction

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

complex, Subsection Assemblage

dividing, Subsection Assemblage Assemblage

fundamental principal, Assemblage

lowest common denominator (

*see*lowest common denominator)multiplying, Assemblage Assemblage

reducing, Paragraph

reducing an algebraic fraction, Assemblage

simplify, Assemblage

unlike, Subsection

function, Paragraph Definition

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 equationsgeneral form for a linear equation, Definition

general quadratic form

of a circle, Paragraph

geometric formulas, Assemblage

golden rectangle, Exercise

graph, Definition Definition Item

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 growthhalf-life, Subsection Paragraph Assemblage

half-plane, Paragraph

horizontal line, Paragraph Assemblage Item

slope of, Assemblage

hyperbola, Paragraph Section Paragraph Definition Definition Paragraph

asymptotes, Paragraph

branches, Paragraph

central, Assemblage Paragraph

conjugate axis, Paragraph

translated, Assemblage

transverse axis, Paragraph

vertices, Paragraph

imaginary number, Paragraph Assemblage

imaginary unit.

*See**i*\(\thinspace\)inconsistent, Item

inconsistent system.

*See*system of equationsincreasing function, Paragraph Paragraph Item Subsection Paragraph.

*See also*increasing graphincreasing graph, Paragraph

independent system.

*See*system of equationsindex (of a radical), Paragraph Paragraph Assemblage

inequality, Note

compound, Note Caution Assemblage

graphical solution, Subsection Subsection

linear, Subsection Assemblage Paragraph

quadratic, Subsection Assemblage

strict, Paragraph

system of, Subsection

infinity (\(\infty\)), Paragraph

initial value, Item Assemblage Assemblage Item Paragraph Item

input variable.

*See*functionintercept, Definition.

*See also**x*-intercept;*y*-interceptintercept 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 variationirrational numbers, Paragraph

laws of exponents, Assemblage

LCD.

*See*lowest common denominatorlead coefficient, Definition Assemblage

least-squares regression line, Paragraph Subsection

like fractions, Paragraph

adding or subtracting, Subsection Assemblage Assemblage

like radical, Paragraph

line

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 reductionlinear 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 equationlinear 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 equationslogarithmic function, Paragraph

logarithmic scale, Paragraph.

*See also*logarithmlogarithms

common (base 10), Paragraph

clearing fractions with, Paragraph

finding the, Assemblage

lowest common multiple (LCM), Example

major axis.

*See*ellipsemathematical model, Assemblage

maximum value, Note.

*See also*parabolamechanistic models, Paragraph

midpoint, Paragraph Assemblage

minimum value, Note.

*See also*parabolaminor axis.

*See*ellipsemodel, Assemblage

empirical, Paragraph

mechanistic, Paragraph

Moore's law, Paragraph

muliplying algebraic fractions, Assemblage

multiplicity, Paragraph

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 notationopposite of a binomial, Subsection

ordered triple, Paragraph

outliers, Item.

*See also*linear regressionoutput variable.

*See*functionparabola, Subsection Paragraph Paragraph Paragraph

axis of symmetry, Item

maximum value, Note

minimum value, Note

vertex form, Subsection Assemblage

vertex of, Assemblage

parallel lines, Subsection Item

percent decrease, Subsection

percent increase, Subsection

perfect square, Paragraph

perpendicular lines, Subsection Item

pH scale, Paragraph

point-slope form, Paragraph.

*See also*point-slope formulapoint-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 rootpower function, Paragraph Section Definition Definition Subsection Subsection Assemblage Caution

vs exponential function, Subsection

vs exponential functions, Assemblage

principal, Assemblage

principal root, Paragraph.

*See also*rootproduct 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

proportional

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

radical, Paragraph Assemblage

exponential notation, Subsection Assemblage

like radicals, Paragraph

quotient rule for, Assemblage

rationalizing the denominator, Subsection

simpifying, Subsection

sums and differences of, Subsection

radicand, Paragraph

radius, Paragraph Assemblage.

*See also*circlerate, Assemblage

rate of change, Subsection Definition.

*See also*sloperatio method, Paragraph

rational exponents, Assemblage Assemblage

rational expression, Paragraph.

*See also*algebraic fractionrational function, Subsection Paragraph

rationalizing the denominator, Paragraph Subsection.

*See also*radicalreducing fractions, Subsection Paragraph Assemblage Assemblage

regression.

*See*linear regressionregression line, Paragraph.

*See also*linear regressionRichter scale (or magnitude), Subsection Paragraph

root

cube root, Definition

of negative numbers, Subsection

of powers, Assemblage

of real numbers, Assemblage

principal root, Paragraph

scaling exponent, Paragraph

scaling property of direct variation, Subsection

scatterplot, Item

scientific notation, Subsection Assemblage

second-degree.

*See*quadraticsimplifying a complex fraction, Assemblage

coordinate formula for, Assemblage

of a line, Definition

rate of change, Assemblage

undefined, Assemblage

zero, Assemblage

slope-intercept form, Subsection Assemblage

slope-intercept formula.

*See*slope-intercept formsolution, 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

of a negative real number, Paragraph (

*see also*imaginary number)starting value.

*See*initial valuestrict inequality, Paragraph

substitution method.

*See*system of equationssum or difference of fractions, Subsection Assemblage Assemblage Assemblage

supply equation, Paragraph

of a cone, Assemblage

of a cylinder, Assemblage

of a pyramid, Assemblage

of a sphere, Assemblage Item

symmetry.

*See*axis of symmetrysystem of equations

\(2\times 2\), Paragraph

\(3\times 3\), Subsection Subsection Assemblage

back-subsitution, Subsection

consistent and independent, Definition

dependent, Definition Assemblage Paragraph Paragraph

elimination method, Subsection Assemblage Subsection

Gaussian reduction, Subsection Assemblage

graphing, Subsection

inconsistent, Subsection Definition Assemblage Paragraph Paragraph

independent, Definition

involving conic sections, Subsection

linear combination, Paragraph Subsection

solution, Paragraph Definition Subsection

substitution method, Subsection

triangular form, Paragraph

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*hyperbolatriangular form.

*See*system of equationsvariation.

*See*direct variation; inverse variationvaries directly, Assemblage Assemblage

varies inversely, Assemblage Assemblage

vertex

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 line, Paragraph Assemblage Item

slope of, Assemblage

vertical line test.

*See*functionvertices.

*See*ellipse; hyperbola; system of inequalitiesof 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