Monday, March 7, 2011
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.
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
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.
-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
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
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