Download Sections 9.1/9.2 Notes: Inverse Variations *A function of the form or

Sections 9.1/9.2 Notes: Inverse Variations
k
*A function of the form y  or xy  k , where x  0 , is an inverse variation.
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Example 1: Modeling Inverse Variation
a) Suppose that x and y vary inversely, and x = 3 when y = -5. Write the function that models the
inverse variation.
b) Suppose that x and y vary inversely, and x = 0.3 when y = 1.4. Write the function that models
the inverse variation.
Example 2: Identifying Direct and Inverse Variation
Is the relationship between the variables in each table a direct variation, an inverse variation, or
neither? Write functions to model the direct and inverse variations.
a)
b)
c)
*The graphs of inverse functions have two parts.
Example 3: Graphing an Inverse Function
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Draw a graph of y  .
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*The graph has two parts. Each part is called a ______________________.
*The x-axis is a horizontal __________________ and the y-axis is a vertical _______________.
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*When k is positive, the branches of y  are in Quadrants I and III. When k is negative, then
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branches are in Quadrants II and IV.
*You can use asymptotes to graph translations of inverse variations.
Properties: Translations of Inverse Variations
k
k
 c is a translation of y  by b units horizontally and c units vertically.
The graph of y 
x b
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The vertical asymptote is x = b. The horizontal asymptote is y = c.
Example 4: Graphing a Translation
1
 3.
a) Sketch the graph of y 
x2
b) Sketch the graph of y  
1
3.
x7
*If you know the translations or asymptotes of the graph of an inverse variation, you can write
the equation.
Example 5: Writing the Equation of a Translation
Write an equation for the translation of the given equation with the given asymptotes.
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a) y  , asymptotes at x  2 and y  3 .
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1
b) y   , 4 units to the left and 5 units up.
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