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Reciprocal Functions

                 1
1. Graph y           .
                 x
x        y
0        1
             = undefined
         0
1
2
10
100
0.5
0.1
0.01

                1
When x is 0,         is _______________.
                x
                         1                                                      1
When x is positive,          is _______________.          When x is negative,       is
                         x                                                      x
_______________.
                              1                                                     1
When x becomes large,              _______________.       When x approaches 0,
                               x                                                    x
_______________.

Steps:
         1. Vertical Asymptotes
         2. Signs
         3. Invariant & Other Important Points

                                                1
2. Given y       f x , as shown, graph y              .
                                              f x
2                                               1
3. Given f x      x       1 , graph y   f x    and y                       .
                                                                  f x


                                                                                    10

                                                                                     8

                                                                                     6

                                                                                     4

                                                                                     2


                                              -10       -8       -6       -4   -2        2   4   6   8   10
                                                                                    -2

                                                                                    -4

                                                                                    -6

                                                                                    -8

                                                                                -10


                                                    1
4. Given y     f x , as shown, graph y                       .
                                                f x
1                                      1
5. Given f x       x   2 , graph y   f x    and y             .
               2                                     f x




                                                          1
6. Given f x   x x     2 , graph y    f x    and y                .
                                                      f x

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Reciprocal functions

  • 1. Reciprocal Functions 1 1. Graph y . x x y 0 1 = undefined 0 1 2 10 100 0.5 0.1 0.01 1 When x is 0, is _______________. x 1 1 When x is positive, is _______________. When x is negative, is x x _______________. 1 1 When x becomes large, _______________. When x approaches 0, x x _______________. Steps: 1. Vertical Asymptotes 2. Signs 3. Invariant & Other Important Points 1 2. Given y f x , as shown, graph y . f x
  • 2. 2 1 3. Given f x x 1 , graph y f x and y . f x 10 8 6 4 2 -10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 -6 -8 -10 1 4. Given y f x , as shown, graph y . f x
  • 3. 1 1 5. Given f x x 2 , graph y f x and y . 2 f x 1 6. Given f x x x 2 , graph y f x and y . f x