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29 Cards in this Set
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Natural numbers/counting numbers (N)

{1,2,3...}


Whole numbers (W)

{0,1,2...}


Integer numbers (Z)

{...2,1,0,1,2...}


Rational numbers (Q)

Can be express in form m/n where m and n are real numbers and n is not equal to 0 (terminating or repeating decimals)


Irrational numbers (I)

All nonterminating or nonrepeating decimals


Real numbers (R)

All rational and irrational numbers


Closure Property

a+b is a real number; ab is a real number


Commutative Property

a+b=b+a; ab=ba


Associative Property

(a+b)+c=a+(b+c); (ab)c=a(bc)


Identity Property

a+0=a; a*1=a


Inverse Property

a+(a)=0; a*(1/a)=1


Distributive Property

a(b+c)=ab+ac


Opposite Numbers

Two numbers that are the same distance from the origin on a number line but on different sides


How to find the xintercept

Set y=0 and solve for x


How to find the yintercept

Set x=0 and solve for y


Slope Intercept Form

y=mx+b; m is the slope and b is the y intercept


Standard Form

ax+by=c


Absolute Value Graphs

y=x+b, where b shifts the graph up or down that many units; y=x+b, where b shifts the graph left or right that many units (in opposite direction)


Find the vertex of an absolute value equation

1. Set the expression in the absolute value bars equal to 0 and solve for the variable. It will represent the x value.
2. Plug the x value into the original equation to find a point. 

What does f(x) mean?

y=


Domain

The set of all numbers that allow a function to be defined (x values)


Range

The set of all numbers that are y values of a function


To solve for a domain:

1. If there is a variable in the denominator, set the denominator not equal to 0 and solve for x.
2. If there is a square root, set the expression under the square root greater than or equal to 0 and solve for x. 3. If there is a square root in the denominator, set the expression greater than 0 and solve for x. 4. In most other cases, the domain is the set of real numbers. 

To solve for range:

Solve the function for x and use the same procedure as you would for finding the domain.


Linear Programming

Goal is to find optimization value. Use vertices to determine the maximum or minimum value of the objective quantity


Steps to finding the maximum or minimum objective quantity

1. Graph the system in order to determine the variables.
2. Evaluate the objective quantity at each vertex. 3. Not all objective quantities will have both a maximum and a minimum. 

Matrices

Written as rows by columns, or M x N


Determinate A

Use your calculator


Compound Interest

A=P(1+(r/n))^NT
A – the amount in bank after T years P – principle (initial amount), also A0 R – interest rate (decimal) N – number of time compounded per year T – how many years 