1. ## range of graph

Hello, I have graphed the following equation:
y= 1/(x-1)

and I have figured out the domain (-infinity,1) U (1, +infinity), but I don't know what the range is and how to get it?
I know some main points as (2,1) and (-1, -.5) and (0,-1).
Thank you!

2. Originally Posted by ss103
Hello, I have graphed the following equation:
y= 1/(x-1)

and I have figured out the domain (-infinity,1) U (1, +infinity), but I don't know what the range is and how to get it?
I know some main points as (2,1) and (-1, -.5) and (0,-1).
Thank you!
The range is $\displaystyle \mathbf{R}\backslash\{0\}$.

You can easily check this by noting that if you let $\displaystyle y=0$ you can not solve for $\displaystyle x$.

3. asymtotic to x =1, as stated above. take a look at the graph

4. y = 1/(x - 1), at x = 1, y is undefined. Better graph below,

5. thanks! so is the range (-infinity,0) U (0, +infinity) ?

6. Originally Posted by ss103
Hello, I have graphed the following equation:
y= 1/(x-1)

and I have figured out the domain (-infinity,1) U (1, +infinity), but I don't know what the range is and how to get it?
sometimes, a good way to find the range of a function is to find the domain of the function's inverse ...

$\displaystyle y = \frac{1}{x-1}$

$\displaystyle x = \frac{1}{y-1}$

$\displaystyle y-1 = \frac{1}{x}$

$\displaystyle y = \frac{1}{x} + 1$

domain of the inverse = range of the original function is all reals except 0