Index

A

Abel, Niels Henrik

Absolute value:

definition of (||)

as distance on the number line

equations involving

as a function

of a function

inequalities involving

properties of

Acute angle

Adjacent side (adj)

Addition of two sinusoidal functions

Algebraic expression

Algebraic function

Ambient temperature

Ambiguous case (Law of Sines)

Amplitude:

of cosine graphs

of sine graphs

Angle(s):

acute

central

complementary

coterminal

definition of

of depression

of elevation

initial side of

obtuse

quadrantal

reference

right

in standard position

straight

supplementary

terminal side of

vertex of

Angular measure:

degrees

minutes

negative

positive

radians

seconds

Angular speed

Annuity

Aphelion

Apogee

Apollonius

Apolune

Approaching infinity:

from the negative direction (x → −∞)

from the positive direction (x → ∞)

Approaching a number:

from the left (x → a⁻)

from the left and the right (x → a)

from the right (x → a⁺)

Approximating the zeros of a function

Arc length on a circle

Arccosecant function

Arccosine function

Arccotangent function

Arcsecant function

Arcsine function

Arctangent function

Area of an isosceles triangle

Area under a graph

Arithmetic combinations of functions:

definition of

domain of

Arithmetic mean

Asymptotes:

of exponential functions

finding

horizontal

of a hyperbola

of logarithmic functions

oblique

of rational functions

slant

of trigonometric functions

vertical

Auxiliary rectangle

Average

Axis (axes):

conjugate of a hyperbola

coordinate

major of an ellipse

minor of an ellipse

of a parabola

transverse of a hyperbola

Axis of symmetry

B

Bascule bridge

Base:

change of

of an exponential function

of a logarithmic function

Bearing

Beer-Lambert-Bouguer law

Bell-shaped curve

Bifolium

Binomial

Binomial expansions

Bounds:

for cosine function

for sine function

Brachistochrone

Branches:

of a hyperbola

of a rational function

C

Cancellation property

Carbon dating

Cardioid

Cardiovascular branching

Cartesian coordinate system:

axes of

coordinates of a point in

defined

distance formula in

origin of

quadrants in

translation in

in 3-space

in 2-space

Cartesian plane

Cassegrain telescope

Catenary

Carrying capacity

Ceiling function ([x])

Celsius to Fahrenheit conversion

Celsius to Kelvin conversion

Center:

of a circle

of an ellipse

of a hyperbola

Central angle

Change in x

Change in y

Change-of-base formula

Circle:

arc length on a

center of

definition of

graph of

parametric equations of

polar equation of

radius of

rectangular equation of

standard form of

unit

Circular functions

Circular helicoid

Circular helix

Circumference of the Earth

Closed curve

Closed interval

Comet Halley

Common logarithm

Complementary angles

Complete Factorization Theorem

Completing the square

Complex numbers:

conjugate of

definition of

imaginary part of

real part of

Composition of functions:

definition of

domain of

Compound interest

Compression of a graph

Conditional trigonometric equations

Conic section:

applications of

definition of

directrix of

eccentricity of

focus of

in polar coordinates

polar graphs of

relationship to a double-napped cone

rotated in polar coordinates

Conjugate axis of a hyperbola

Conjugate of a complex number

Conjugate factor

Conjugate hyperbolas

Conjugate Zeros Theorem

Constraint

Constant function

definition of

domain of

Constant term of a polynomial function

Continuous compound interest

Continuous function

Conversions:

degrees to radians

logarithm to a natural logarithm

polar coordinates to rectangular coordinates

polar equation to rectangular equation

radians to degrees

rectangular coordinates to polar coordinates

rectangular equation to a polar equation

Convex limaçon

Coordinate(s):

line

plane

of a point in the Cartesian coordinate system

of a point of the number line

of a point in the polar coordinate system

Coordinate line

Cosecant function:

asymptotes of

cycle of

definition of

domain of

graph of

inverse of

odd

period of

range of

signs

values of

Cosine function:

amplitude of

bounds for

cycle of

definition of

domain of

double-angle formula for

even

graph of

half-angle formula for

inverse of

period of

phase shift of

range of

signs of

sum and difference formulas for

values of

x-intercepts of

zeros of

Cosines, Law of

Cotangent function:

asymptotes of

cycle of

definition of

domain of

graph of

inverse of

odd

period of

range of

signs of

values of

x-intercepts of

Coterminal angles

Cycle:

of cosecant graph

of cosine graph

of cotangent graph

of the graph of a periodic function

of secant graph

of sine graph

of tangent graph

Cycloid:

definition of

parametric equations of

Cubic function

Curie, Marie

D

Decay constant

Decay, exponential

Decay rate

Decibel

Decimal form of a real number

Decreasing function

Definite integral

Degree measure of an angle

Degree of a polynomial function

Degree to radian conversion

Dependent variable

Depreciation

Depression, angle of

Derivative of a function

Descartes, René

Difference formula:

for the cosine

for the sine

for the tangent

Difference of functions:

definition of

domain of

Difference quotient

Difference of two cubes

Difference of two squares

Differential calculus

Dimpled limaçon

Directrix:

of a conic section

of a parabola

Discontinuous function

Discriminant

Disjoint intervals

Distance:

between numbers on the number line

between points in the plane

Distributive law

Dividend

Divisible

Division Algorithm:

for polynomials

for real numbers

Division of fractions

Divisor

DMS notation

Domain:

of an arithmetic combination of functions

of a composition of functions

definition of

of an exponential function

of a hyperbolic function

implicit

of a linear function

of a logarithmic function

of a polynomial function

of a power function

of a quadratic function

of a rational function

of trigonometric functions

Double-angle formulas:

for cosine

for sine

for tangent

Double-napped cone

Drug concentration

E

e:

definition of

numerical value of

Eccentricity:

of a conic section

of an ellipse

of a hyperbola

of an orbit

of a parabola

E. Coli bacteria

Effective half-life

Elevation, angle of

Eliminating the parameter

Ellipse:

applications of

center of

definition of

eccentricity of

focal width of

foci of

length of major axis

major axis of

minor axis of

polar equation of

reflection property of

standard form of

vertices of

End behavior

Endpoints of an interval

Equation of motion

Equation in two variables:

definition of

equivalent

graph of

satisfying

solution set of

Equilibrium position

Equivalent equations

Equivalent inequalities

Eratosthenes

Euler, Leonhard

Even function

Existence of a limit

Expansion of a binomial

Exponent

Exponential equations

Exponential function:

asymptote of

base of

definition of

domain of

graphs of

natural

one-to-one property of

properties of

Exponential mathematical models

Exponents, laws of

Extraneous solutions

Extrema, relative

F

Factor Theorem

Factored expression

Factorial function

Factorization:

of the difference of two cubes

of the difference of two squares

of a polynomial

of the sum of two cubes

Fahrenheit scale

Family of lines

Ferrari, Lodovico

Floor function ([x])

Focal chord

Focal width

Focus:

of a conic section

of an ellipse

of a hyperbola

of a parabola

Fontana, Niccolo

Fractional expression:

additional of

definition of

Freely falling object

Frequency of simple harmonic motion

Function:

absolute value

algebraic

arccosecant

arccosine

arccotangent

arcsecant

arcsine

arctangent

ceiling

compositions of

constant

continuous

cosecant

cosine

cotangent

cubic

decreasing

definition of

derivative of

difference of

discontinuous

domain of

even

exponential

factorial

floor

graph of

greatest integer

horizontal line test

hyperbolic cosine

hyperbolic secant

hyperbolic sine

hyperbolic tangent

implicit domain of

increasing

inverse

inverse hyperbolic cosine

inverse hyperbolic secant

inverse hyperbolic sine

inverse hyperbolic tangent

inverse trigonometric

linear

logarithmic

natural exponential

natural logarithmic

notation for

objective

odd

one-to-one

periodic

piecewise-defined

polynomial

postage stamp

power

product of

quadratic

quartic

quintic

quotient of

range of

rational

reciprocal

relative extrema of

secant

sine

square root

squaring

sum of

tangent

transcendental

turning point of

undefined at a number

vertical line test for

zeros of

Fundamental Theorem of Algebra

Future value

G

Galileo

Gateway Arch

Gauss, Carl Friedrich

Generation time

Geocentric parallax

Global behavior

Global positioning system

Gompertz curve

Graph(s):

of an absolute value function

of arccosine function

of arcsine function

of arctangent function

bell-shaped

branches of a

of a circle

compression of

of a constant function

of cosecant function

of cosine function

of cotangent function

cycle of

decreasing

of an ellipse

end behavior of

of an equation

of exponential functions

of functions

hole in a

horizontal asymptote of

horizontal compression of

horizontal line

horizontal shift of

of a hyperbola

of hyperbolic cosine function

of hyperbolic sine function

increasing

of an inequality

intercepts of

of an inverse function

of a linear function

of logarithmic functions

nonrigid transformation of

of one-to-one functions

of a parabola

points of intersection of

of polar equations

of polynomial functions

of power functions

of a quadratic function

reflections of

rigid transformation of

of secant function

of sine function

slant asymptote of

stretch of

symmetry of

of tangent function

vertical asymptote of

vertical line

vertical shift of

vertical stretch/compression of

Greater than (>)

Greater than or equal to (≥)

Greatest integer function ()

Growth, exponential

Growth constant

Growth rate

H

Half-angle formula:

for cosine

for sine

for tangent

Half-life:

effective

of a medicine

of a radioactive substance

Half-open interval

Halley’s comet

Harmonic motion

Hohmann transfer

Hole in a graph

Horizontal asymptote:

definition of

for graphs of exponential functions

for graphs of rational functions

Horizontal compression

Horizontal line, equation of

Horizontal line test

Hypatia

Hyperbola:

applications of

asymptotes of

auxiliary rectangle for

branches of

center of

conjugate

conjugate axis of

definition of

eccentricity of

focal width of

foci of

length of transverse axis

polar equation of

rectangular

reflection property of

standard form of

transverse axis of

vertices of

Hyperbolic cosine

Hyperbolic secant

Hyperbolic sine

Hyperbolic tangent

Hypotenuse (hyp)

I

i (imaginary unit)

Iceman (Ötzi)

Identities:

definition of

hyperbolic

trigonometric

Image of x

Imaginary part of a complex number

Implicit domain of a function

Improper fraction

Increasing function

Independent variable

Indeterminate form

Index of summation

Inequalities:

definition of

equivalent

graph of

involving absolute values

linear

nonlinear

properties of

simultaneous

solution set of

Inequality symbols

Infinity symbols (∞ and −∞)

Initial point on a plane curve

Initial population

Initial side of an angle

Input

Integral, definite

Integral calculus

Intensity level of sound

Intercepts of a graph

Interest:

compound

continuous

simple

Intermediate Value Theorem

Intersection of sets (∩)

Interval(s):

closed

disjoint

endpoints of

graphs of

half-open

notation

open

unbounded

Interval notation

Inverse of a function:

definition of

domain of

methods for finding

properties of

range of

Inverse trigonometric functions:

definitions of

properties of

Irrational numbers

Irreducible quadratic

K

Kelvin scale

Kepler, Johannes

Kepler’s first law of planetary motion

Knots

L

Lascaux cave drawings

Law of Cosines

Law of Sines

Law of universal gravitation

Laws of exponents

Laws of logarithms

Leading coefficient of a polynomial

Legs of a right triangle

Leibniz, Gottfried Wilhelm

Lemniscate

Less than (<)

Less than or equal to (≤)

Libby, Willard

Lighthouse of Alexandria

Limaçon

Limits:

evaluating

existence of

indeterminate form of

notation for

trigonometric

Line(s):

family of

graphs of

horizontal

intercepts of

parallel

perpendicular

point-slope form of

points of intersection of

slope of

slope-intercept form of

vertical

Linear depreciation

Linear equation:

in three variables

in two variables

Linear function:

definition of

domain of

Linear speed

Local behavior

Local extremum:

definition of

maximum

minimum

Logarithmic equations

Logarithmic function:

asymptote of

common

definition of

domain of

equations involving

graph of

natural

one-to-one property of

properties of

Logarithmic mathematical models

Logarithms, laws of

Logistic function

LORAN

Losing solutions

M

Mach number

Major axis of an ellipse

Malthus, Thomas R.

Mathematica

Mathematical model

Maximum

Midpoint of a line segment:

in the plane

on the real number line

Minimum

Minor axis of an ellipse

Minus infinity

Minutes

Monomial

Mormon Tabernacle

Multiplicity of a zero

N

Napier, John

Natural exponential function:

definition of

domain of

graph of

one-to-one property of

properties of

Natural logarithmic function:

definition of

domain of

graph of

one-to-one property of

properties of

Natural numbers

Nautical mile

Negative direction (x→ − ∞)

Negative real numbers

Newton, Isaac

Newton’s law of cooling/warming

n-gon, regular

Nonnegative real numbers

Nonrepeating decimals

Nonrigid transformation of a graph:

definition of

vertical compression

vertical stretch

Nonstrict inequalities

NSAID

Number:

complex

integers

irrational

natural

rational

real

Number line

Number of zeros of a polynomial

O

Objective function

Oblique asymptote

Oblique triangle

Obtuse angle

Octagon

Odd function

One-to-one function:

definition of

inverse of

One-to-one property

Open interval

Opposite side (opp)

Ordered pair

Orientation on a plane curve

Origin:

in the coordinate plane

on the number line

symmetry with respect to

Output

P

Parabola:

applications of

axis of

definition of

directrix of

eccentricity of

focal chord

focal width of

focus of

graph of

intercepts of

polar equation of

reflection property of

standard form of

vertex of

Paraboloid

Parallel lines

Parameter

Parameterization

Parameterized curve

Parametric equations:

of a circle

conversion of a polar equation to

conversion of a rectangular equation to

of a cycloid

definition of

of a line

Partial fraction decomposition

Partial fractions

Pascal’s triangle

Pendulum clock

Perigee

Perihelion

Perilune

Period:

of the cosecant function

of the cosine function

of the cotangent function

definition of

of the secant function

of the sine function

of the tangent function

Period of simple harmonic motion

Periodic function:

cycle of

definition of

Perpendicular lines

Petals of rose curves

pH of a solution

Phase shift

Piecewise-defined functions

Plane curve

Planetary orbits

Plotting points

Point:

coordinates of

as an ordered pair

plot of

Point-slope equation of a line

Points of intersection of graphs:

in polar coordinates

in rectangular coordinates

Polar axis

Polar coordinate system:

conventions in

coordinates of a point in

definition of

relationship to rectangular coordinates

Polar equation:

of a cardioid

of a circle

of a conic

conversion to parametric equations

of an ellipse

of a hyperbola

of a lemniscate

of a limaçon

of a line through the origin

of a parabola

of a rose curve

of a rotated graph

of a spiral curve

Pole

Polygon

Polygon, regular

Polynomials:

coefficients of

constant

constant term of

definition of

degree of

division of

domain of

end behavior of

factors of

graphs of

leading coefficient of

linear

local behavior of

quadratic

quartic

quintic

rational zeros of

single term

zero

Population growth

Positive direction (x → ∞)

Positive real numbers

Postage stamp function

Power function:

catalogue of graphs

definition of

Present value

Product of functions:

definition of

domain of

Product-to-sum formulas

Proper fraction

Proper rational expression

Pythagorean identities

Pythagorean theorem

Q

Quadrantal angles

Quadrants

Quadratic, irreducible

Quadratic formula

Quadratic function

definition of

standard form of

Quartic function

Quintic function

Quotient

Quotient of functions:

definition of

domain of

R

R, the set of real numbers

Radian to degree conversion

Radian measure of an angle

Radicand

Radioactive decay

Radius of a circle

Radon

Range of a function:

definition of

finding

Rational function:

definition of

discontinuous

domain of

graph of

Rational number

Rational zeros of a polynomial

Rational Zeros Theorem

Rationalization:

of a denominator

of a numerator

Ray

Real numbers

Real part of a complex number

Reciprocal function

Reciprocal trigonometric functions

Rectangular coordinate system

Rectangular hyperbola

Reference angle

Reflecting surfaces

Reflection of a graph:

in x-axis

in y-axis

in y = x

Reflection property:

of an ellipse

of a hyperbola

of a parabola

Refraction of light

Regular n-gon

Regular partition

Relative extremum

Relative maximum

Relative minimum

Remainder

Remainder Theorem

Repeated zero

Repeating decimals

Restricted domains

Richter, Charles F.

Richter scale

Right angle

Right triangle:

definition of

solving a

trigonometry

Rigid transformation of a graph:

definition of

horizontal shifts

reflections

vertical shifts

Rise

Robotic arm

Rose curves

Root of an equation

Run

S

Sample points

Satisfying an equation

Secant function:

asymptotes of

cycle of

definition of

domain of

even

graph of

inverse of

period of

range of

signs

values of

Secant, hyperbolic

Secant line

Seconds

Sector

Semicircles

Semi-ellipse

Set-builder notation

Set(s):

intersection of

interval notation for

union of

Shifted graphs

Shroud of Turin

Sigma notation

Sign-chart method

Sign properties of products

Signs of trigonometric functions

Simple closed curve

Simple harmonic motion

Simple interest

Simple zero

Simultaneous inequality

Sine function:

amplitude of

bounds for

cycle

definition of

domain of

double-angle formula for

graph of

half-angle formula for

inverse of

odd

period of

phase shift of

range of

signs of

sum and difference formulas for

values of

x-intercepts of

zeros of

Sines, Law of

Single-term polynomial function

Slant asymptote(s):

definition of

finding

of a hyperbola

Slope

Slope function

Slope-intercept equation of a line

Slope of a secant line

Slope of a tangent line

Snell’s law

Solution:

of an equation in two variables

of an inequality

Solution set

Solving right triangles

Sorensen, Soren

Space curve

Spiral of Archimedes

Spring constant

Square, completing the

Square root function

Square root of −1

Squaring function

Standard form of an equation:

of a circle

of an ellipse

of a hyperbola

of a parabola

of a sphere

Standard position of an angle

Statuary Hall

Step functions

Straight angle

Stretch of a graph

Strict inequalities

Sum formula:

for the cosine

for the sine

for the tangent

Sum of functions:

definition of

domain of

Sum-to-product formulas

Sum of two cubes

Summation notation

Supplementary angles

Symmetry:

of a graph

with respect to the line y = x

with respect to the origin

with respect to x-axis

with respect to y-axis

tests for in polar coordinates

tests for in rectangular coordinates

Synthetic division

T

Tangent, hyperbolic

Tangent function:

asymptotes of

cycle of

definition of

domain of

double-angle formula for

graph of

inverse of

odd

period of

range of

signs of

sum and difference formulas for

values of

x-intercepts of

Tangent line:

to a circle

equation of

to the graph of a function

slope of

Tartaglia (Nicola Fontana)

Tautochrone

Terminal point on a plane curve

Terminal side of an angle

Terminating decimals

Tests for symmetry of a graph:

in polar coordinates

in rectangular coordinates

Transcendental functions

Transverse axis of a hyperbola

Triangle inequality

Triangles, solving

Trigonometric equations

Trigonometric functions:

of angles

cycle of

domains of

even-odd properties of

exact values of

graphs of

inverses of

periods of

Trigonometric identity

Trigonometric substitution

Trigonometry:

right triangle

unit circle

Turning point

U

Unbounded:

behavior of a function

in the negative direction (x → − ∞)

in the positive direction (x → ∞)

Unbounded interval

Undefined slope

Union of sets (∪)

Unit circle

Unit circle trigonometry

V

Value of a function

Values of trigonometric functions

Variable:

dependent

independent

Verhulst, P.F.

Vertex:

of an angle

of an ellipse

of a hyperbola

of a parabola

Vertical asymptote:

definition of

finding

for graphs of logarithmic functions

Vertical compression of a graph

Vertical line, equation of

Vertical line test

Vertical shift of a graph

Vertical stretch of a graph

W

Whispering gallery

Witch of Agnesi

X

x-axis:

definition of

reflection in

symmetry with respect to

x-coordinate

x-intercept

xy-plane

Y

y-axis:

definition of

reflection in

symmetry with respect to

y-coordinate

y-intercept

Z

Zero(s):

approximating

complex

conjugate pairs of

of cosine function

of a function

finding

of multiplicity m

number of

rational

real

the real number

repeated

simple

of sine function

of tangent function

Zero polynomial