"Unizor: Math 4 Teens - Algebra - Function Graphs - Lecture 2" - Information and Links:

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"Unizor: Math 4 Teens - Algebra - Function Graphs - Lecture 2" and the language of the book is English.


“Unizor: Math 4 Teens - Algebra - Function Graphs - Lecture 2” Metadata:

  • Title: ➤  Unizor: Math 4 Teens - Algebra - Function Graphs - Lecture 2
  • Author:
  • Language: English

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  • Internet Archive ID: ➤  Unizor_Math4Teens_Algebra_FG_002

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"Unizor: Math 4 Teens - Algebra - Function Graphs - Lecture 2" Description:

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What happens with a graph if we multiply an argument of a function? In other words, how will a graph of a function y = f(k*x) look? Using similar approach, if a point (A,B) belongs to an original graph (i.e. B = f(A)) then (A/k,B) belongs to a graph of a new function. Indeed, let's substitute x = A/k and y = B to a new function: f(k*(A/k)) = f(A) = B which proves that (A/k,B) belongs to a graph of a new function. Geometrically, the fact that for each point (A,B) of an original graph there is a point (A/k,B) of a new graph means that an entire original graph is "squeezed" towards an Y-axis by a ratio of k. The word "squeeze" is really applicable to cases of k >= 1. When 0 < k < 1 it is really a "stretch". For k = -1 this transformation is a reflection relative to a Y-axis because for any point (A,B) on the original graph the point (-A,B) belongs to a graph of a new function y = f(-x). Finally, a transformation for any negative k is a reflection relative to a Y-axis and a horizontal "squeeze" or "stretch". How will a graph of a function change if we add a positive constant to a function? In other words, if you know how a graph of a function y = f(x) looks, what will be a graph of a function y = f(x) + a? Using a similar approach as before, assume that a point (A,B) belongs to an original graph (i.e. B = f(A)). Then, obviously, a point (A,B+a) belongs to a graph of a new function because it satisfies its algebraic expression: B+a = f(A) + a. It means, that a graph of a new function y = f(x) + a can be obtained by shifting an old graph up (for positive constant a) or down (for negative a). Finally, if we multiply a function by a constant (i.e. consider a new function y = k*f(x)) its graph will be "stretched" or "squeezed" in a vertical direction. The reason is, if a point (A,B) belongs to an original graph (i.e. B = f(A)) then (A,k*B) belongs to a new graph since k*f(A) = k*B

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  • Added Date: 2010-07-26 04:49:49

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