Functions

Even Functions

Even Functions

f(-x) = f(x)

Odd Functions

f(-x) equals -x

Piecewise Function

A function made up of multiple functions on domains so that each input has exactly 1 output

y = f(x) +/- k

shifts y up/down

y = a * f(x)

stretches y by a; if >1, will stretch, if <1, will compress, if <0, inverts over x axis

y = f(x + h)

Shifts y left/right

y = f(b * x)

Dilates the x-values; 3x divides all values by 3, 1/5x multiplies all values by 5

AROC

f(b) - f(a) / b - a

Negative Leading Coefficient

Even function’s ends point down; odd function begins in upper left square rather than lower left square

Point of Inflection

The point of transition between concave up and concave down

Concave Up

The ends of a graph point down, with the middle bowed up

Concave Down

The ends of a graph point up, with the middle bowed down

Secant Line

A line passing through two points of the curve of a function (slope equivalent to AROC)

y = mx + b

slope-intercept form

y = m(x - x1) + y1

point-slope form

Quadratic Functions

Classic curve function; AROCs of AROC are constant

The Greatest Integer Function

Function that chops off decimals and only considers sig figs at the ones place or above

Degree

greatest exponent of a polynomial

Leading Coefficient

the coefficient of the variable with the highest exponent

Multiplicity of One

Graph passes linearly through the x-axis at that point

Even Multiplicity

Graph bounces at the x-axis at that point

Odd Multiplicity

Graph is locally cubic (curves weird) at the x-axis at that point

Successive Differences

taking the AROC of the AROC until you get a constant number; the amount of AROCs will be equal to the degree of the polynomial

Pascal’s Triangle

Pyramid of multiplicities which displays the patterns of coefficients in binomials

Countdown Pattern in Expanded Binomials

As you go from left to right or right to left, the exponents of either x or y (depending on direction) will count down from the original exponent to 0

First Coefficient Rule

The first and last non-one coefficients in an expanded binomial will always be equal to the exponent of the original binomial

AROC

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