# Functions

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Even Functions

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## Tags and Description

### 27 Terms

1

Even Functions

f(-x) = f(x)

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2

Odd Functions

f(-x) equals -x

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3

Piecewise Function

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

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4

y = f(x) +/- k

shifts y up/down

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5

y = a * f(x)

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

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6

y = f(x + h)

Shifts y left/right

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7

y = f(b * x)

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

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8

AROC

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

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9

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

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10

Point of Inflection

The point of transition between concave up and concave down

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11

Concave Up

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

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12

Concave Down

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

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13

Secant Line

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

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14

y = mx + b

slope-intercept form

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15

y = m(x - x1) + y1

point-slope form

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16

Classic curve function; AROCs of AROC are constant

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17

The Greatest Integer Function

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

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18

Degree

greatest exponent of a polynomial

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19

the coefficient of the variable with the highest exponent

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20

Multiplicity of One

Graph passes linearly through the x-axis at that point

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21

Even Multiplicity

Graph bounces at the x-axis at that point

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22

Odd Multiplicity

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

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23

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

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24

Pascal’s Triangle

Pyramid of multiplicities which displays the patterns of coefficients in binomials

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25

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

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26

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

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27

AROC

Average Rate of Change

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