# Graph each function and include the graph's tables. Identify the domain and range;and compare the graph with the graph of y=`(1)/x` y=`(-10)/x` y=`1/(x+3)+3`

embizze | Certified Educator

(1) Compare `y=-10/x` to `y=1/x` :

`x`                `1/x`               `-10/x`
__________________________

-3                `-1/3`              `10/3`

-2                `-1/2`               5

-1                -1                10

0               undef            undef

1                   1                -10

2                   `1/2`             -5

3                  `1/3`              `-10/3`

The graph of `y=-10/x` is the graph of `y=1/x` transformed by a vertical stretch of factor 10 and a reflection across the horizontal axis.

The graph of `y=1/x` in red; `y=-10/x` in black:

(2) Compare `y=1/(x+3)+3` to `y=1/x` :

The graph of `y=1/(x-h)+k` is the graph of `y=1/x` translated h units horizontally and k units vertically. In this case we move the graph 3 units left and 3 units up.

`x`                         `1/x`                           `1/(x+3)+3`

-3                         `-1/3`                           undef

-2                          `-1/2`                          4

-1                          -1                            `7/2`

0                            undef                      `10/3`

1                             1                            `13/4`

2                            `1/2`                             `16/5`

3                            `1/3`                             `19/6`

The graph of `y=1/x` in red; `y=1/(x+3)+3` in blacK: