Transformation
A change in the location or specific shape of a parent function, without changing its general shape
Rigid transformation
A change in the location only ofthe graph of a function
Non-Rigid transformation
Creates a distortion of the specific shape of a graph, without changing its basic shape
Relation
Any set of ordered pairs often described by an equation
Function
Set of ordered pairs where each input has one output ( two inputs can have the same output and still be a funtion)
Domain
Set of all input values x
Range
set of all output values y
Independent variable
input variable usually x
Dependent variable
output variable usually y
One-to-one function
function where each input has one unique output.
Pise-wise function
The function has different definitons for different parts of the domain.
Difference Quotient
f(x+h) -f(x) / h
Rene Descartes
French philosopher and mathematician who created the Cartesian Coordinate Plane
Average Rate of Change
The slope of the secant line formed by any two points on the graph of a function.
Even Function
A functiont that has y-axis symmetry
Hyperbola
The name for the graph of the reciprocal function
Roots
The x-values for which f(x)=o
linear Parent Function
f(x)=x straight line
Squaring (quadratic) function
f(x)=x*2 u shape
Cubic parent funtion
f(x)=x*3 curved line
Square root function
f(x)=Square root of x half of line
Reciprocal parent function
f(x)= 1/x hyperbola graph two curves on opposite sides
Greatest integer function
f(x)= [[x]] dot with line then open dot
absolute value function
f(x)= lxl
General form of a Circle
(x-h)2+(y-k)2=r*2
Point slope form of a linear equation
y-y=m(x-x)
Zero Factor property
IF axb=0 then a=0 or b=0
extraneous solution
Value for the variable that opccurs in the solving an equation, but does not satisfy the origonal equation.
Perfect square trinomial
product of (a+b)^2=a^2+2ab+b^2
Quadratic
ax^2+bx+c
Parabla
the name for a graph of the quadratic function
Odd function
f(-x)=-f(x)
Standard form of a linear equation
Ax+By=C
Remainder theorm
If f(x)=0, then x-k is a factor of f(x)
Multiplicity
The # of times a value is the root of a polynomial function
Intermediate value theorm
If f(x) is a polynomial function then it takes on every value from f(xsub1) to f(xsub2) on the interval [ x1,x2]
Continuous
A graph with no breaks, gaps, or holes
Pure imaginary number
a number of the form a+bi, where a=0
The fundamental theorm of algebra
If f(x) is a polynomial of degree n, then f(x) has at least one complex root, not necessarily imaginary.
Complex number
a+bi
Conjugate root theorm
If a+ the square root of b, is a root of the polynomial then so is a- the square root of b
real number
a+0i
imaginary number
a+bi
standard form for a quadratic
y=a(x-h)^2+k
Odd multiplicity
pass through
even multiplicity
touch turn arroumd
higher multiplicity
becomes fatter
Eulers number the natural base
as n->infintie, (1+1/n)^n
Transcendental function
Any function that cannot be expressed as a polynomial with rational coefficients
Algebriac function
Any function that can be expressed as a polynomial with rational coefficients
Exponential function
a function of the form f(x)=a^x where 0<a<1
Angle in standard form
An angle whose vertex is at the origin of the coordinate plane, and begins on the positve x-axis opening "up and to the left
Trigonmetry
measures of triangles
Positve angle
an angle in the coordinate palne that opens counter-clockwise
Terminal side
the ray to which an angle opens
Radian
and angle measure equivalent to one "radius" length around a circle
Change of base formula
logaX= logbX / logb a
The horizontal line test
any function with an inverse will meet this requirement
Phase shift
the term that indicates that a periodic function has been translated left or right
amplitude
half of the distance between the minumum and maximum output values of a sine or cosine funtion