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43 Cards in this Set

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natural numbers
1,2,3,4,5...etc
whole numbers
0,1,2,3,4,5...etc
integers
negative infinity...infinity NO decimals and NO fractions
rationals
a ratio of two integers, all fractions, terminating / repeating decimals.
irrationals
pi, square root of 2, e, square root of x.
real numbers
anythign except square root of a negative.
additive inverse
3+-3=0
OPPOSITES
the sum of a number and its additive inverse is zero.
absolute value
distance from zero on a number line. numbers are always positive.
distributive
a(x+y)=
ax+ay
OR
bc+bd+be=
b(c+d+e)
identity:
additive
multiplicative
add. = a + 0 = a

mult. = a * 1 = a
Inverse:
additive
multiplicative
add.= a + -a = 0

mult= a * 1/a = 1
Commutative:
add

mult
add. = a+b=b+a

mult. = a*b=b*a
associative:
add.

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

mult.= a(bc) = b(ac) = c (ab)
<
less than, AND, intersection

(less thAND)
>
greater than, OR, union
(greatOR)
standard form
Ax+By=C
ABC= integers
A>0
slope-intercept form
y=mx+b
point-slope form
y-y1= m (x-x1)
(x,y,) = point on line
m= slope
x
y
variables
x= independent
y= dependent
table method
x y
-1
0
1

with slope-intercept form, use the numbers int he x-colum for x, and solve for y.
intercept method
*you must find both x and y intercept*
x-intercept= set y=0
y-intercept= set x=0
vertical line
slope=infinite
horizontal line
slope=0
parallel lines
same slope
never intersect
different y-intercepts
perpendicular lines
slopes are opposite inverse
EX) 3, -1/3
solid line
inclusive, less than or equal to..etc
dashed line
exclusive, less than, not equal to,
union
OR, greater than, combining everything in both equations
intersection
AND, less than, just the overlap
dependent variable...
varies with independent
function is...
a special type of relation wehre x-values do not repeat.
function-
vertical line test
if you draw a vertical line at any point, and two points cross the line, it is not a function.
function-
f(x) <-- the function value at x.
domain
the set of all possible input values (independent values, x-values)
range
the set of possible output values, (dependent variable, y-values)
linear function
f(x)=x<-- base function
absolute value function
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
quadric function
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)
shifts:
vertical
y=f(x)+a <--move up a spaces

y=f(x)-a <-- move down a spaces
shifts:
horizontal
y=f(x-a)<-- move left a spaces

y=f(x+a) <-- move right a spaces
f(xsquared)
graph (0,0), (1,1) (4, 2)
reflection over x axis:
y=-f(x)
reflection over y axis:
y=f(-x)