Can someone explain domain and range of a function

The domain is all the possible x values

and

The range is all the range is all the posible y vlues.

 

You can often get it just by looking at or thinking about the curve.

Sometimes you must look at the eqation and look at what values x or y can, or cannot take.

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for instance

 

y-2 =1/x

 

You cannot divide by 0 so x is not zero

so the domain is all real x where x is not equal to 0      

\(Domain:\:x\in R\;\;where\;\; \:x\ne0\;\;\)

 

1 divided by anything is not equal to 0 so y-2 is not equal to 0 so    y is not equal to 2

\(Range:\:y\in R\;\;where\;\; \:y\ne2\;\;\)

 

So x=0 and y=2 are the asymptotes of this hyperbola.