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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 non-terminating or non-repeating 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 x-intercept Set y=0 and solve for x How to find the y-intercept 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