# 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`

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### 1 Answer

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

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

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-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: