Monday, March 7, 2011

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http://www.khanacademy.org/#browse

Parent Functions

http://learn.uci.edu/oo/getOCWPage.php?course=OC0111113&lesson=004&topic=13&page=1

Remainders and Factors

If the remainer is 0 when one polynomial is divided by another polynomial, the divisor and the quotient are factos of the dividend.

Graph Changes

The graph of g(x)=f(x)-c is the graph of f shifted downward c units.

The graph of g(x)=f(x+c) is the graph of f shifted c units to the left.

The graph of g(x)=f(x-c) is the grapg of f shifted c units to the right.

The graph of g(x)=-f(x) is the graph of f reflected across the x-axis.

The graph of g(x)=f(-x) is the graph of f reflected across the y-axis.

The graph of g(x)=c X f (x) is the graph of f stretched or compressed vertically by a factor of c.

The graph of g(x)= f(c X x) is the graph of f stretched or compressed horzontally by a factor of 1/c.

Functions and Inverses

If f is a function, the following statements are equivalent:
  • the inverse of f is a function
  • f is one to one
  • the graph of f passes the horizontal line test
the inverse function, if it exists, is written as f^-1 where if y=f(x) then x=f^-1(y)

Function

A function consists of:
  • a set of inputs, called the domain
  • a rule by which each input determines one and only one output
  • a set of outputs called the range

Chapter Two Basics

When f is a function and a is a real number, the following are equivilant statements:
-a is a zero of the function y=f(x)
-a is an x-intercept of the graph of f
-a is a solution, or root, of the equation f(x)=0

The only number whose square root is a zero is zero itself.

A fraction is zero only when its numerator is zero and its denominator is nonzero.

Chapter One Basics

A sequence is an ordered list of numbers.

A sequence is defined recursively if the first term is given and there is a method of determining the nth term by using the terms that precede it.

A sequence is defined explicitly if terms are determined by their position.

An arithmetic sequence is a sequence in which the difference between each term and the preceding term is a constant.

Recursive form: Un=Un-1+d

Explicit form: Un=U1+ (n-1)d

Parallel Lines have equal slopes.

The product of the slopes of perpendicular lines is -1.

The difference between an actual data value and a predicted data value is called a residual.

The correlation coefficent has the same sign as the slop of the least squares regression line.

A geometric sequence is a sequence in which terms are found by multiplying a preceding term by a nonzero constant r.

From Holt Precalculus: A Graphing Approach

Distance Problem Part Three

Distance Problem Part TWO

Distance Problem Part One

Compound Intrest with ln

Ln Problem

Ln Problems

Natural Logarithms

Log Examples PART TWO and Equvilant Statements

Logs and some Examples

End of Bacteria Problem

Continuous Compounding and Bacteria Growth Problem

Continous Compounding with the Number e