Math Final

Front 1

natural numbers

Back 1

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

Front 2

whole numbers

Back 2

0,1,2,3,4,5...etc

Front 3

integers

Back 3

negative infinity...infinity NO decimals and NO fractions

Front 4

rationals

Back 4

a ratio of two integers, all fractions, terminating / repeating decimals.

Front 5

irrationals

Back 5

pi, square root of 2, e, square root of x.

Front 6

real numbers

Back 6

anythign except square root of a negative.

Front 7

additive inverse

Back 7

3+-3=0
OPPOSITES
the sum of a number and its additive inverse is zero.

Front 8

absolute value

Back 8

distance from zero on a number line. numbers are always positive.

Front 9

distributive

Back 9

a(x+y)=
ax+ay
OR
bc+bd+be=
b(c+d+e)

Front 10

identity:
additive
multiplicative

Back 10

add. = a + 0 = a

mult. = a * 1 = a

Front 11

Inverse:
additive
multiplicative

Back 11

add.= a + -a = 0

mult= a * 1/a = 1

Front 12

Commutative:
add

mult

Back 12

add. = a+b=b+a

mult. = a*b=b*a

Front 13

associative:
add.

mult.

Back 13

add. a+ (b+c)= b+(a+c) = c+ (a+b)

mult.= a(bc) = b(ac) = c (ab)

Front 14

<

Back 14

less than, AND, intersection

(less thAND)

Front 15

>

Back 15

greater than, OR, union
(greatOR)

Front 16

standard form

Back 16

Ax+By=C
ABC= integers
A>0

Front 17

slope-intercept form

Back 17

y=mx+b

Front 18

point-slope form

Back 18

y-y1= m (x-x1)
(x,y,) = point on line
m= slope

Front 19

x
y
variables

Back 19

x= independent
y= dependent

Front 20

table method

Back 20

x y
-1
0
1

with slope-intercept form, use the numbers int he x-colum for x, and solve for y.

Front 21

intercept method

Back 21

*you must find both x and y intercept*
x-intercept= set y=0
y-intercept= set x=0

Front 22

vertical line

Back 22

slope=infinite

Front 23

horizontal line

Back 23

slope=0

Front 24

parallel lines

Back 24

same slope
never intersect
different y-intercepts

Front 25

perpendicular lines

Back 25

slopes are opposite inverse
EX) 3, -1/3

Front 26

solid line

Back 26

inclusive, less than or equal to..etc

Front 27

dashed line

Back 27

exclusive, less than, not equal to,

Front 28

union

Back 28

OR, greater than, combining everything in both equations

Front 29

intersection

Back 29

AND, less than, just the overlap

Front 30

dependent variable...

Back 30

varies with independent

Front 31

function is...

Back 31

a special type of relation wehre x-values do not repeat.

Front 32

function-
vertical line test

Back 32

if you draw a vertical line at any point, and two points cross the line, it is not a function.

Front 33

function-

Back 33

f(x) <-- the function value at x.

Front 34

domain

Back 34

the set of all possible input values (independent values, x-values)

Front 35

range

Back 35

the set of possible output values, (dependent variable, y-values)

Front 36

linear function

Back 36

f(x)=x<-- base function

Front 37

absolute value function

Back 37

f(x)=|x|
D= (-infinity, infinity)
R= {0, infintiy)
graph looks like a V,
Label- (0,0), (-1,1), (1,-1)

X Y
-3 3
-1 1
0 0
3 3
4 4

Front 38

quadric function

Back 38

f(x)=x squared

X Y
-3 9
-2 4
-1 1
0 0
1 1

D= (-infinity, infinity)
R=[0, infinity)

Label (-1,1), (0,0), (-1,1)

Front 39

shifts:
vertical

Back 39

y=f(x)+a <--move up a spaces

y=f(x)-a <-- move down a spaces

Front 40

shifts:
horizontal

Back 40

y=f(x-a)<-- move left a spaces

y=f(x+a) <-- move right a spaces

Front 41

f(xsquared)

Back 41

graph (0,0), (1,1) (4, 2)

Front 42

reflection over x axis:

Back 42

y=-f(x)

Front 43

reflection over y axis:

Back 43

y=f(-x)