Massive Quizlet Precalculus
power function
a function of the form y=ax^b, where a is a real number and b is a rational number
rational function
a function whose rule can be written as a rational expression
Horizontal Asymptote
a horizontal line that the curve approaches but never reaches
infinite limit
a limit in which f(x) increases or decreases without bound as x approaches c
cycloid
a line generated by a point on a circle rolling along a straight line
transverse axis
a line running laterally, across the body (from side to side)
common logarithm
a logarithm with base 10
natural logarithm
a logarithm with base e
nonsingular matrix
a matrix that is invertible
Cramer's Rule
a method that uses determinants to solve a system of linear equations
digits and common logarithms
a positive number K has (n+1) digits if and only if log K is in the interval [n, n+1)
arithmetic sequence
a sequence in which each term is found by adding the same number to the previous term
geometric sequence
a sequence in which each term is found by multiplying the previous term by the same number
finite sequence
a sequence that comes to an end
infinite sequence
a sequence that continues without end
annuity
a series of equal regular deposits
identity matrix
a square matrix that, when multiplied by another matrix, equals that same matrix
principal axis
a straight line perpendicular to the surface of a mirror that divides the mirror in half
Descartes' Rule of Signs
a technique for finding the number of positive and negative roots to a polynomial equation with real coefficients
directly proportional
a term used to describe the relationship between two variables whose graph is a straight line passing through the point (0,0)
permutation
an alteration; a rearrangement of elements, especially in mathematics
polar equation
an equation expressed in terms of polar coordinates
hyperbola
an open curve formed by a plane that cuts the base of a right circular cone
discriminant
b^2-4ac
orientation
beginning
polynomial factors
if divide polynomial by equation and do not get remainder then is a factor
Conjugate Pairs Theorem
in a polynomial function, if (a+bι) is a zero, then (a-bι) is a zero
change of base formula
logbM=logcM/logcb
apparent magnitude
m2 -m1 =2.5 log a(b1/b2)
Richter scale
m=log(I/I 0)
rotation of axes
one of the steps in coordinate transformation involving a rotation of the meridian of the reference coordinate system
direction of increasing parameter
path of particle thats moving
Domain of f⁻¹
range of f
varies inversely
relationship between two variables whose graph forms a curve that slopes downward from left to right
arc length formula
s=rθ
Even/Odd Identities
sin(-x) = - sin x cos(-x) = cos x tan (-x) = - tan x csc (-x) = - csc x sec (-x) = sec x cot (-x) = - cot x
Double Angle Formulas
sin(2x)=2sin(x)cos(x) cos(2x)=cos^2-sin^2 =1-2sin^2 =2cos^2-1 tan(2x)=2tanx/1-tan^2
sum and difference formulas for sine
sin(u+v)=sin u cos v+cos u sin v sin(u-v)=sin u cos v-cos u sin v
Power-Reducing Formulas
sin^2 x = (1 - cos 2x)/(2) cos^2 x = (1 + cos 2x) tan^2 x = (1 - cos 2x)/(1 + cos 2x)
Pythagorean Identities
sin^2x+cos^2x=1 1+tan^2x=sec^2x 1+cot^2x=csc^2x
Product to Sum Formulas
sinx sin y = 1/2 [cos(x - y) - cos(x + y)] cosx cos y = 1/2 [cos(x - y) + cos(x + y)] sinx cos y = 1/2 [sin(x + y) + sin(x - y)] cos x sin y = 1/2 [sin(x + y) - sin(x - y)]
Pythagorean Identity
sin²θ + cos²θ = 1
Reciprocal Identities
sinθ = 1/cscθ ; cscθ = 1/sinθ cosθ = 1/secθ ; secθ = 1/cosθ tanθ = 1/cotθ ; cotθ = 1/tanθ
derivative
something that comes from another source
Sum Formula for Tangent
tan(A+B)=tanA+tanB/1-tanAtanB
Difference Formula for Tangent
tan(A-B)=(tanA-tanB)/(1+tanAtanB)
Quotient Identities
tanθ = sinθ/cosθ cotθ = cosθ/sinθ
reference angle
the acute angle formed by the terminal side of an angle in standard position and the x-axis
terminal point
the ending point of a vector
parabola
the graph of a quadratic function
the graph of f(x)=ax^2 is obtained from
the graph of the squaring function s(x)=x^2
index of summation
the letter used in the summation symbol sigma
nominal rate
the original interest rate
Sign of Polynomial Function
the polynomial function p(x) will have a constant sign on each interval formed by the real zeros of p(x) plotted on a number line.
Number of Combinations
the product of the number of things of each type
the squaring function s(x)=x^2
the quadratic function F(x)=ax^2+bx+c with a=1 ,b=0, c=0
minor axis
the shorter axis of an ellipse
initial point
the starting point of a vector
value of an annuity
the sum of all payments and interest
domain of sine and cosine
(-∞,∞)
conic
(geometry) a curve generated by the intersection of a plane and a circular cone
arithmetic progression
(mathematics) a progression in which a constant is added to each term in order to obtain the next term
parameter
(n.) a determining or characteristic element; a factor that shapes the total outcome; a limit, boundary
standard form for equation of a circle
(x-h)^2 + (y-k)^2 = r^2
Horizontal Ellipse
(x-h)^2/a^2 + (y-k)^2/b^2 = 1
Find the vertex of f(x)=ax^2+bx+c, a=-0
1.find x-coordinate h=-b/2a of the vertex 2.calculate k=f(-b/2a) to find its y-coordinate
conjugate axis
2b
Period of Sine and Cosine Functions
2π
Latus Rectum of Parabola
4p
Graph of a Quadratic Function
A U-shaped curve called a parabola
focus of a parabola
A fixed point F used with a directrix to define a parabola
Number of zeros theorem
A function defined by a polynomial of degree n has at most n distinct zeros
Quadratic Function
A function that can be written in the form f(x) = ax2+bx+c, where a,b,and c are real numbers and a ≠ 0
quadratic function
A function that can be written in the form f(x) = ax2+bx+c, where a,b,and c are real numbers and a ≠ 0
graph of an equation
A graph of the set of ordered pairs that are solutions of the equation.
secant line
A line that intersects a circle in two points
parametric equations
A pair of equations that define the x and y coordinates of a point in terms of a third variable called a parameter.
Factor Theorem
A polynomial f(x) has a factor x - k if and only if f(k) = 0
Binomial Theorem
A way in which to write binomials in expanded form
compound interest
A=P(1+r/n)^nt
complex zero
According to the Fundamental Theorem, every polynomial function has at least one...
matrix equation
An equation in which the variable is a matrix.
logarithmic equation
An equation that contains one or more logarithms
area of a sector
Area of a Sector = (central angle/360) x πr²
general form of the equation of a line
Ax + By + C = 0
Decomposition of a function
Bringing a function back to its base form
Fundamental Theorem of Algebra
Every polynomial equation with degree greater than zero has at least one root in the set of complex numbers.
rational zeros theorem
For any polynomial function, with integral coefficients, if P/Q is a zero, then P is a factor of the constant and Q is a factor of the leading coefficient.
Trigonometric Functions
Functions that manipulate quantitative data in a worksheet.
Amplitude
Height of a wave
simple interest
I=prt
binomial coefficient
The number of ways of arranging k successes among n observations
lowest terms
When a fraction is expressed with the fewest possible pieces, it is in lowest terms. (Also called simplest form.)
slant asymptote
When the degrees of the numerator is ONE larger than the denominator
Complex polynomial
When we want to emphasize that complex numbers may be used in this way,
range of sine and cosine
[-1,1]
the unit circle
a circle with a radius of 1, centered at the origin, x^2+y^2=1
polynomial function
a continuous function that can be described by a polynomial equation in one variable
determinant of a 2x2 matrix
ad/bc
lower limit
bottom of the range of possible values that a measurement on a quantitative variable can have
sum and difference formulas for cosine
cos(u+v)=cos u cos v-sin u sin v cos(u-v)=cos u cos v+sin u sin v
Distance Formula
d = √[( x₂ - x₁)² + (y₂ - y₁)²]
rectangular equation
equation in terms of x and y
mutually exclusive events
events that cannot happen at the same time
Odd function
f(-x)=-f(x)
Odd functions
f(-x)=-f(x)
Even function
f(-x)=f(x)
Even functions
f(-x)=f(x)
standard form of a quadratic function
f(x) = ax^2 + bx + c
natural exponential function
f(x)=e^x
Identity function
f(x)=x
Difference Quotient
f(x+h)-f(x)/h
Inverse Function notation
f^-1(x)
foci
fixed points at the centers of an ellipse
Polynomial Inequality
has the general form f(x) < 0 or f(x) > 0
focal diameter
length of latus rectum
Tangent as slope
m=tan0-
(n/r)
n!/r!(n-r)!
relative frequency
number of times an allele occurs in a gene pool compared with the number of times other alleles occur
exponential form
numbers written with exponents
eccentricity
oddness
cartesian
of or pertaining to Descartes
the graph of g(x)=ax^2 is the reflection
of the graph of f(x)=|a|x^2
Partial Fractions
one of the fractions that was added or subtracted to result in a given rational expression
pH scale formula
pH=-log[H+]
vertical asymptote
set denominator equal to zero
plane curve
set of points that can be drawn without lifting the pencil
Cofunction Identities
sin (π/2 - x) = cos x cos (π/2 - x) = sin x tan (π/2 - x) = cot x cot (π/2 - x) = tan x sec (π/2 - x) = csc x csc (π/2 - x) = sec x
Sum to Product Formulas
sin x + sin y = 2sin(x + y)/(2) cos(x -y)/(2) sin x - sin y = 2cos(x + y)/(2) sin (x - y)/(2) cos x + cos y = 2cos(x + y)/(2) cos(x - y)/(2) cos x - cos y = -2 sin(x + y)/(2) sin(x - y)/(2)
Half Angle Formulas
sin x/2 = + or - √(1 - cos x)/2 cos x/2 = + or - √1 + cos x)/2 tan x/2 = (1 - cos x)/(sin x) or (sin x)/(1 + cos x)
circular functions
trigonometric functions of an angle defined using the unit circle
inverse function
two functions f and g are inverse functions if and only if both of their compositions are the identity function
coding matrix
way to see coding intersections between two lists of items in your project
Leontief input-output model
x = Cx + d
Basic Trigonometric Functions
x =a+2np or x =1p-a2 +2np x =a+2np or x =12p-a2 +2np x =a+np
two-intercept form
x/a + y/b = 1
general form of the equation of a circle
x^2+y^2+ax+by+c=0
standard form of the equation of a hyperbola
x^2/a^2-y^2/b^2=1
general equation of a parabola
y = a(x - h)2 + k
Equation of a tangent line
y-y1=m(x-x1)
direct variation
y=kx
joint variation
y=kxz
The amplitude of a sine wave is its:
zero to maximum
inversely proportional
A term used to describe the relationship between two variables whose product is constant.
singular matrix
A singular matrix is a square matrix with no inverse. It's determinant is zero.
general equation of an ellipse
(x-h)^2/a^2 + (y-k)^2/b^2 = 1
Vertical Ellipse
(x-h)^2/b^2 + (y-k)^2/a^2 = 1
standard equation of a parabola
(x-h)^2=4p(y-k)
midpoint formula
(x₁+x₂)/2, (y₁+y₂)/2
Reflecting Property of Ellipses
A ray of light originating at one focus will be reflected to the other focus
Fibonacci sequence
A sequence of numbers in which each number is the sum of the preceding two.
geometric progression
A sequence of numbers in which the ratio of one number to its predecessor is always the same
Remainder Theorem
If a polynomial f(x) is divided by x-k, the remainder is r=f(k)
reduction formula
If α is an angle in standard position whose terminal side contains (a,b), then for any real number x: a sin x + b cos x = √(a² + b²) sin(x + α)
major axis
Line through the widest part of an ellipse
the additive rule
P(A or B) = P(A) + P(B) - P(A and B)
probability of the complement
P(A') = 1 - P(A)
experimental probability
Probability that is based on repeated trials of an experiment
Particular Term in a Binomial Theorem
Term containing the factor x^r in expansion of (x+y)ⁿ is (ⁿₙ-r)x^r(yⁿ⁻r)
vertices
The point of intersection of two sides of a polygon. The point of intersection of three edges of a space figure.
Parameterization
The process of choosing values for the parameters in a model.
Multiplicative Inverse
The reciprocal of a number
power growth model
The regression line and power model are shown with their corresponding scatterplots
Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
branches
The two symmetrical parts of a hyperbola
Fundamental Counting Principle
Uses multiplication of the number of ways each event in an experiment can occur to find the number of possible outcomes in a sample space.
Theoretical Probability
What should occur or what we expect to happen in an experiment
directrix
a fixed line that is equidistant from the vertex as the focus is to the vertex
logarithmic function
a function of the form f(x)=logbX, where b≠1 and b>0, which is the inverse of the exponential function f(x)=b^X
upper limit
the top of the range of possible values that a measurement on a quantitative variable can have