Posted by **Matt-** on Monday, November 1, 2010 at 5:26pm.

I have a question-

The range of y = 1/(x-5) is All real Numbers

True or False

I think it is false because it should be all real numbers except y shouldn't equal 0. Is that correct or don't I understand it-Please explain if I'm wrong.

Thanks

- Algebra II -
**Reiny**, Monday, November 1, 2010 at 6:31pm
you are correct,

If you graph it, the graph will approach the x-axis , but will never reach it.

For large positive values of x, the graph will be slightly above the x-axis,

for large negative values of x, the graph will be slightly below the x-axis

if you solve

0 = 1/(x-5) and cross-multiply , you get

0 = 1 which of course is a contradiction. Thus our equaiton cannot have a solution, that is, y can never be zero.

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