60 terms

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