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Chapter 8 Inverses and Radicals

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Chapter 8 Inverses and Radicals Powered By Docstoc
					Chapter 8: Inverses and
       Radicals
Lesson 2: Inverses of Relations

         Mrs. Parziale
        What is a Function?
• A      relation              is a set of ordered
  pairs.
•
  A function                   is a relation with
  ordered pairs whose x-coordinate has only
   one      y-coordinate.
• What test can you apply to the graph of a
  relation to see if it is a function?
      Vertical line test
                   Function or Not?
• Graph the following relation on
  the coordinate grid:
  f = { (1,4), ),(2, 8) , ( 3, 8), (0, 0),
  (1, -4)}
• Is it a function?
• Create a new function g by
  switching the x and y
  coordinates of f.
  g=
• Is it a function?
• What is the line of symmetry for
  f and g?
                         Inverses
  Definition:
  The inverse of a relation is the relation obtained by reversing the
  order of the x and y coordinates
  in each ordered pair in the relation.


• The domain of a relation is the set of all possible values
  for the         x                coordinate
• The range of a relation is the set of all possible values of
  the        y              coordinate.

• In the examples on the previous slides how do the
  domain of f and the range of g compare?
• …the range of f and the domain of g?
    Inverse Relation Theorem
Suppose f is a relation and g is the inverse of f. Then:
1) A rule for g can be found by switching        x and y.

2) The graph of g is the reflection image of the graph of f
   over the line
                  y=x

3) The domain of g is the range            of f, and the
  range of g is the  domain of f.
                   Example 1
• Let g = { (4, 3), (0, -1), (5, 2), (-8, -1)}
• a) Is g a function? Why of why not?
• b) Identify the inverse of g.

• c) Is the inverse of g a function? Why or
  why not?

The inverse of a relation is always a relation. But the
inverse of a function is not always a function          .
• Graph the function: y = 3x +2
• Complete the chart for coordinates on the graph.


x    (x,y) Inverse of y =3x + 2
                    (y,x)

0

1

-1


 • Graph the inverse of y = 3x + 2
 • What is the equation of the inverse of y = 3x +2
 • Is the inverse a function?
       Theorem ( Horizontal Line Test for
                  Inverses)
The inverse of a function f is itself a function if and only if
no       horizontal           line intersects the graph of f in
more than one point.

Determine if the inverse of a function is a function. Explain your reasoning.

       a)                        b)                  c)
                  Closure
• How can the inverse of a relation be found
  from the coordinates of the relation?
• Explain how the graphs of any relation f an
  its inverse are related?
• Give the equation for the inverse of the
  relations:
     y = 3x – 2          y = 9x2 +12x - 6

				
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posted:2/5/2013
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