Graphing Inverse Variations

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Graphing Inverse Variations
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• A relationship that can be written in the form y
  k/x , where k is a nonzero constant and x ?
  0, is an inverse variation.
• The constant k is the constant of variation.
• Inverse variation implies that one quantity will
  increase while the other quantity will decrease
  (the inverse, or opposite, of increase).

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• The domain is all real numbers except zero.
• Why?

Since x is in the denominator, the only
restriction we would have is any numbers we cant
divide by. The only number we cannot divide by is
zero.
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The range is all real numbers except zero.
Why?
Since k is a nonzero number, and x is a nonzero
number, there is NO WAY y will ever be zero!
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Since both the domain and range have restrictions
at zero, the graph can never touch the x and y
axis.
This creates asymptotes at the axes.
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• The graphs of inverse variations have two parts.
• Ex. f(x) 1/x
• Each part is
• called a
• branch.

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• When k is positive, the branches are in Quadrants
  I and III.
• When k is negative, the branches are in Quadrants
  II and IV.

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• Translations of Inverse Variations
• The graph of y
• is a translation of y k/x, b units
  horizontally and c units vertically.
• The vertical asymptote is x b. The horizontal
  asymptote is y c.

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Translations of Inverse Variations The graph
of y
k tells us how far the branches have been
stretched from the asymptotes. We can use it to
help us find out corner points to start our
branches.
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• Example

Vert. Asy. ? 3 Horz. Asy.? 4 Quad? 1
3 Distance? 1
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• You Try Graph

Vert. Asy. ? -1 Horz. Asy.? 0 Quad? 2
4 Distance? 2
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• We can also write the equation just given the
  parent function and the asymptotes.
• Ex. Write the equation of y -1/x that has
  asymptotes x -4 and y 5.
• Answer