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Exercise #9
Symmetry, Reflections and Inverses


Reflections

    f ( x)
                         y




                                           x




             f ( x)


        f ( x)



Example
Given f ( x) 3x 4 , write an equation formed by reflecting f ( x) over the:

        a) x-axis


        b) y-axis



Graph each equation.
                         y




                                           x




Homework Exercise 9 #1, 3, 7, 9, 11, 12, 14
Inverse

Inverse functions are denoted by f 1 ( x) .

Example
Given f ( x) 2 x 5 , graph f 1 ( x) .
                                                          To graph or find the inverse of
                                                           f ( x) , switch the x and y values.




Basically, when graphing the inverse of a function, f ( x) is reflected over the line y       x
OR choose points and switch the x and the y values around.
                                                                      y




                                                                                          x




Example
Given the graph of f ( x) below, sketch the graph of f 1 ( x) .

                           y




                                              x




Homework Exercise 9 #2, 8, 13, 16, 18, 19

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Exercise #9 notes

  • 1. Exercise #9 Symmetry, Reflections and Inverses Reflections f ( x) y x f ( x) f ( x) Example Given f ( x) 3x 4 , write an equation formed by reflecting f ( x) over the: a) x-axis b) y-axis Graph each equation. y x Homework Exercise 9 #1, 3, 7, 9, 11, 12, 14
  • 2. Inverse Inverse functions are denoted by f 1 ( x) . Example Given f ( x) 2 x 5 , graph f 1 ( x) . To graph or find the inverse of f ( x) , switch the x and y values. Basically, when graphing the inverse of a function, f ( x) is reflected over the line y x OR choose points and switch the x and the y values around. y x Example Given the graph of f ( x) below, sketch the graph of f 1 ( x) . y x Homework Exercise 9 #2, 8, 13, 16, 18, 19