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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Math-trig4.1-2: Exponential Functions
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 shi- Set (place) – final – Tone: Props – components and position Scene – meaning “十”是打满了结的纪事绳子 “十”造字本义：名词，一根用来打结纪事的绳子，代表满数、全数。从金文开始成为指事字。“十”的甲骨文是象形字，像一根用于纪事的垂悬的绳子。古人用结绳纪事、计数，一根绳子代表一个纪事主题，代表全数。金文承续甲骨文字形。有的金文在绳上加圆点指事符号，表示结绳纪事。有的金文将表示结绳的圆点指事符号写成短横指事符号。篆文承续金文字形。《说文解字》说：十，数之具也。一为东西，丨为南北，则四方中央备矣。：十，表示十进位所需数都已具备。“一”代表世界的东西，“丨”代表世界的南北，“一”和“|”相交成“十”，则表示东西南北中齐备。 十的演变 古人认为十是数字完备的标志，所以“十”又表示完备、齐全、达到极点，如十分、十足。“十全十美”由此而来。又通“什”，指繁杂，如古代的“什锦”也作“十锦”。 汉字中的数，并不像我们想象的就是几个计数的数字。造字本身是一个漫长的过程，其中集合了中国先人的察天识地的深邃智慧，它们深厚的含义融在了中华文化的血脉中，一直影响到现在。 “Ten” is a chronicle rope full of knots The original meaning of the coinage of “ten” is: noun, a rope used to tie a knot to record events, representing a full number and […]
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