Study your flashcards anywhere!
Download the official Cram app for free >
 Shuffle
Toggle OnToggle Off
 Alphabetize
Toggle OnToggle Off
 Front First
Toggle OnToggle Off
 Both Sides
Toggle OnToggle Off
 Read
Toggle OnToggle Off
How to study your flashcards.
Right/Left arrow keys: Navigate between flashcards.right arrow keyleft arrow key
Up/Down arrow keys: Flip the card between the front and back.down keyup key
H key: Show hint (3rd side).h key
A key: Read text to speech.a key
43 Cards in this Set
 Front
 Back
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 

slopeintercept form

y=mx+b


pointslope form

yy1= m (xx1)
(x,y,) = point on line m= slope 

x
y variables 
x= independent
y= dependent 

table method

x y
1 0 1 with slopeintercept form, use the numbers int he xcolum for x, and solve for y. 

intercept method

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

vertical line

slope=infinite


horizontal line

slope=0


parallel lines

same slope
never intersect different yintercepts 

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 xvalues 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, xvalues)


range

the set of possible output values, (dependent variable, yvalues)


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(xa)< 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)
