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29 Cards in this Set
- Front
- Back
Natural numbers/counting numbers (N)
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{1,2,3...}
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Whole numbers (W)
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{0,1,2...}
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Integer numbers (Z)
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{...-2,-1,0,1,2...}
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Rational numbers (Q)
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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)
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Irrational numbers (I)
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All non-terminating or non-repeating decimals
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Real numbers (R)
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All rational and irrational numbers
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Closure Property
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a+b is a real number; ab is a real number
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Commutative Property
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a+b=b+a; ab=ba
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Associative Property
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(a+b)+c=a+(b+c); (ab)c=a(bc)
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Identity Property
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a+0=a; a*1=a
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Inverse Property
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a+(-a)=0; a*(1/a)=1
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Distributive Property
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a(b+c)=ab+ac
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Opposite Numbers
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Two numbers that are the same distance from the origin on a number line but on different sides
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How to find the x-intercept
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Set y=0 and solve for x
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How to find the y-intercept
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Set x=0 and solve for y
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Slope Intercept Form
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y=mx+b; m is the slope and b is the y intercept
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Standard Form
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ax+by=c
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Absolute Value Graphs
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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)
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Find the vertex of an absolute value equation
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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. |
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What does f(x) mean?
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y=
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Domain
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The set of all numbers that allow a function to be defined (x values)
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Range
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The set of all numbers that are y values of a function
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To solve for a domain:
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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. |
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To solve for range:
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Solve the function for x and use the same procedure as you would for finding the domain.
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Linear Programming
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Goal is to find optimization value. Use vertices to determine the maximum or minimum value of the objective quantity
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Steps to finding the maximum or minimum objective quantity
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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. |
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Matrices
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Written as rows by columns, or M x N
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Determinate |A|
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Use your calculator
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Compound Interest
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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 |