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4 way to describe Absolute Values graphs

stretch/shrink

vertical/horizontal/combo

vertex

opens up/down

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slope intercept form

y=mx+b

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slope formula for 2 points

y2-y1/x2-x1

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two things needed for writing the equation of a line

point and slope

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parallel lines have the _______ slope

same

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Perpendicular lines have _________ slopes

opposite reciprocal

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rational

Q

natural+whole+integers+all fractions and terminating decimals

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real

R

natural+whole+integers+rational+irrational

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natural

N

1,2,3,4,5,6,etc...

all positive whole numbers (not 0)

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integers

Z

natural+whole+negative numbers

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irrational

I

non terminating decimals without a pattern

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commutative addition

A+7=7+A

operands can switch places

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associative addition

a+(b+c)=(a+b)+c

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distributive

a(b+c)=a**b+a**c

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identity property of addition

a+0=a

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commutative multiplication

A**7=7**A

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associative multiplication

a**(b**c)=(a**b)**c

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identity multiplication

a*1=a

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inverse addition

a+(-a)=0

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inverse multiplication

a*1/a=1

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matrix

a rectangular structure used to organize data

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identity matrix of addition for a 2x2

[0 0]

[0 0]

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identity matrix of multiplication of multiplication for a 3x3

[1 0 0]

[0 1 0]

[0 0 1]

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what must be true to add matrices together?

they must be the same size

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how might you probe that 2 matrices are inverses of each other?

if you multiply them by each other and get an identity matrix and get multiplicative inverse matrices

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what makes an absolute value equation shrink?

a fraction less than one before the abs. val. box

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what makes an abs.val. box stretch?

a whole number greater than 1 before the box

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dependent system

lines are equal, cross all same points

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inconsistent system

it doesn't cross anywhere

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independent system

crosses one point only

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what is the difference between an equation and an inequality?

inequality has a variety of answers within a range, an equation can be inconsistent, independent, or dependent

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horizontal translation

number inside the box

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vertical translation

number outside the box

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how to find the vertex of an abs. val. equation

opposite of number inside box (x), then outside number (y)

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