Where do you find your domain restrictions in a rational function?

  denominator zeros are excluded

Step-by-step explanation:

The domain is the set of values of the independent variable where the function is defined. A rational function is "undefined" where the denominator is zero.

The exclusions of interest are generally those values of the variable that make any denominator be zero.

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Example:

  f(x) = (2/(x-3)) / (4/(x -6))

has denominators of x-3 and x-6. These are zero for x=3 and x=6, so those two values are excluded from the domain of this function. We observe that the function can be simplified to ...

  f(x) = (x -6)/(2(x -3))

but x=6 remains excluded from the domain because of its effect in the original function definition.

Additional comment

If the rational function includes functions that have domain restrictions (such as square root, for example), then those restrictions apply as well.

Usually, but not always, the rational functions where you're asked about domain are the ratios of polynomials. So, you need to factor or otherwise find the zeros of any denominator polynomials in such functions.

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