Classnotes: 4.3-4.4:| 4.5 Properties Video Lessons 4.3 Logarithmic Functions Introduction to Logarithms Evaluate Logarithms Without a Calculator – Whole Numbers Evaluate Logarithms Without a Calculator – Fractions Evaluate Common Logarithms on a Calculator Evaluate Common Logarithms Without a Calculator Evaluate Natural Logarithms on the Calculator Properties of Logarithms Logarithms: Change of Base Formula Video Lessons 4.4 […]
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Class Notes 4.1-2 Form (a, b; domain, range) Two parent graphs Transformations (a, b, asymptote) Exp fn vs Linear fn (common ratio vs common difference) One-to-one property of exponentials finite and infinite/continuous growth rate (natural exp. Euler’s Number) Applications: Bacteria growth Population growth Appreciation vs Depreciation (Cars, Houses) Compound Interest: Trillion Dollar Equation Video Lessons […]
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Video Lessons 1.7 Inverse Functions Inverse Functions Determine if a Relation Given as a Table is a One-to-One Function Restricting the Domain of functions that are not One-to-One
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Video Lessons 1.1 Functions and Function Notation Introduction to Functions Domain & Range & Graphs Vertical & Horizontal Line Tests Evaluating functions using a Graphing Calculator Toolkit/Parent Functions Video Lessons 1.2 Domain and Range Domain and Range Interval & Set-Builder Notation Toolkit / Parent Functions & Domains Piecewise Function: Interpret & Graph Piecewise Function: […]
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Parent functions The most inner function f(x) — coefficient of x is 1 3-5 points for easy calculation f(2x+1) : consider 2x+1 –> x by (-1) , they by (1/2) Notes: corresponding x (input) and y (output) f(x) = f(2x+1) , smaller input x to make 2x+1 corresponding to x in f(x) Stacking the function […]
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Video Lessons 1.4 Composition of Functions Composite Functions Use a Table: Find Values Use Graphs: Find Values Write a function as the composition of two functions Domain of Composite Functions
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A linear approximate divide and conquer change complex into simple things HOW: approximation which one is simpler: parabola or a line? Can we study a line with infinite ends? — Line segment (between two points) — Domain and Range In reality, we don’t care about a thing if it does not change at all. We […]
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很久以前，小山上的庙里住着一个小和尚。每天早上，小和尚都要到山脚下的小河边去挑水，庙里的水缸总是满满的。 Long time ago, there lived a little monk in a temple on the top of a hill. Every morning, the little monk would go fetch water from the river at the foot of the hill. The water tank in the temple was always full. 很久以前：long time ago 以前：before, ago 曾经：once upon a time 挑：to […]
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Fan Xiaoxuan – Health Song
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Actress – Initial g- Set (place) – final e- Tone: Props – components and position Scene – meaning 刘姓最古老的发源地在今河北唐县。这里是远古洪荒时代高扬巨斧、以刘为图腾、勇敢征服自然的古老刘姓子孙生活、栖息的地方。刘姓有“王者气象”，刘汉王朝构成中华文明的第一个高潮，自此中华民族之主体被称为汉人、汉族，中国的语言文字被称为汉语、汉 字。上帝对刘姓实在太垂青了，他把奠基中华文明基础的重担交给了刘姓子孙。 高扬巨斧——刘姓的最原始根蒂 树有根，水有源。 在福建汀州府一带流传过一首歌谣，其内容是：“张王李赵遍地刘，世世代代传不休。刘家子弟多俊杰，三江南北芳名留。”这歌谣中说的“遍地刘”，是指刘姓者多，分布广。现在，刘姓人口约 7000 万，占全国总人口的 5.38%，是中国的第四大姓。那么这个刘姓氏族是如何产生的呢？ “刘”字的最原始、最根本的含义是指一种“斧钺”。 在远古的传说中，人类和宇宙的创造者——盘古当年用以开天辟地创造宇宙世界的正是一柄神奇的巨斧，也就是“刘”。于是早在远古洪荒时代，我们中华民族中的某一支氏族正是认识和感悟到“刘”这种工具的神圣作用和赫赫威力，便用“刘”来作为本氏族的图腾，开始对他顶礼膜拜。久而久之，“刘”便成为这支氏族区别于其它氏族的血缘徽记，世界上古老的刘氏氏族便形成了。 现在，我们可以把“刘”作为一种精神的象征。“刘”代表的是“斧头精神”，勇于开拓奋进、果敢决断的精神。《易经》上说：“得其资斧，其心不快。”资斧，据《释文》当作“齐斧”，即“利斧”之意。此谓人处逆境，心神不快之时，当有一种利斧精神去铲除一切困难障碍。又说：“丧其资斧，贞凶。”谓人丧失利斧的果断，即有正确的思想或理想，也因缺乏果断不得实现而有遗憾。我刘氏族人，当发扬斧头精神，力求奋进有为，既为社会国家作出贡献，又能为家族增添光彩 The origin of the Liu family, the interpretation of the Liu character, the origin of the Liu character, and the origin of Liu everywhere! […]
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