Mathematical notation

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Function

General relativity

Section 2-1: Relations and Functions Goal: Write the domain and range of afunction in interval notation, inequalities, and set notation. ? Domain (Independent variable, InputvaIue,x)? ?- Of 4) OO't t '? x: (iI)(3)(5 ? Range (dependent variable, output value, y)? ?* oj,,l L4- 00r7J1 4i V' x: (t, I) (3,)?, ) ? Set Notation? ?TE 4 f - s c coIIeq, o ,ftM~, ? Relation? k 4 &QA "V ? Vertical Line Test? Function- L i\ ecA'l xqvf &9rn-M (c) I Cam t- Ivt t ac, Cs). - \ MOM 4\PdY\OVU- *j t it on Me. I \uI I k t yt -rwt c, Onto Function? ea (L44Ul1 or k-nfn nc DomBIt arre i__i__ YZWiclfl ecWcpwi _iIiJ ? flJMM Li. -- Continuous Relation? ?'-.-- k efrvrj l0 wt ?.+ick st t v - ? One-to-One Function? ? tflqt iii o(vlav f1.c$

Note Taking Guide 1.6

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Binary operations

Elementary arithmetic

1.06 Translations Essential Questions After completing this lesson, you will be able to answer these questions: How can translations help me understand how to represent verbal phrases as algebraic expressions? What are the key words and phrases that indicate certain operations? Main Idea (page #) DEFINITION OR SUMMARY EXAMPLE Translation (Pg. 2) English to Algebra Addition Terms ? ___________ Subtraction Terms ? l__________ Multiplication Terms ? ___________ Division Terms ? ___________ EX: 4 times the difference of n and 8 ___________ EX: The area of a triangle is found by taking half of the product of the base times the height ___________ EX: x more than 5 ___________ EX: 9 subtracted from x ___________ EX: 25% of x ___________

Note Taking Guide 1.1

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Abstract algebra

Elementary arithmetic

Binary operations

Elementary mathematics

Number

Numerical Operations Essential Questions After completing this lesson, you will be able to answer the following questions: How are expressions rewritten in simplified form based on the mathematical operations in the expression? What is the correct order for performing mathematical operations in simplifying expressions? Main Idea (page #) DEFINITION OR SUMMARY EXAMPLE Real Numbers(P.1) Natural Number: _______________ integers ____________ Numbers: A member of the set of positive integers or zero Integers: A number that can be written without a fraction or _______________ Rational Numbers: Can include positive/negative fractions and decimals. Irrational Number: Any real number that can not be expressed as a ratio. Adding and Subtracting Integers(P.2)

Implicit Differentiation Simplified

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Calculus

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Calculus

Mathematical analysis

Differential calculus

Gottfried Leibniz

Leibniz's notation

Ordinary differential equations

Non-standard analysis

Differential equation

Inverse functions and differentiation

y + xy = 7x Implicit differentiation? (dy/dx) + (x(dy/dx)+ y(1)) = 7(1) (dy/dx)(x + 1) = 7 - y (dy/dx) = (7 - y) / (x + 1) Easy?

Add+Subtract Rational Expressions

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Elementary arithmetic

CNote

Homework ???????????????Grade?8 Name:?___________________________________________ Date:?__________ The?LCM?of?two?rational?algebraic?expressions?is?often?used?to?add?or?subtract?the?two? expressions.?The?method?used?is?to?identify?all?common?factors?in?the?denominator?of? the?expressions,?and?multiply?the?numerators?by?the?uncommon?factors?(exactly?like?you? would?for?non?algebraic?fractions).? Add?or?subtract?the?following?expressions,?by?first?finding?the?LCD. 1. ????a???+????????a?+?x??????+???ax????? ???????????x???a?????x2?+?ax?+?a2??????x3???a3 2. ??1?????+??????5?????+???? ??x? ??????? ?? ???????????x?+?1????4x?+?4????x2???1 ?? 3. ????1?????+?????2x??????+???3x????+????x??????? ??????????3x???3??????(x???1)2???x?+?1?????(x?+?1)2?

Calculator Help Directory

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Office equipment

Logarithms