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State the domain for each of the functions below.

  1. We all know that is excluded from the denominator of a fraction. What value of , if any, would make the denominator ?

  1. Consider the domain of each part of the subtraction problem separately.
    Since  is the difference between  and , both excluded values must be excluded from .

  1. Typically, a square root function has a domain of , but in this case, is squared... meaning both positive or negative values will yield positive outputs. However, do not neglect to consider the .
    What values of , both positive and negative, will make ?

  1. Consider the domain of the numerator and the domain of the denominator separately.
    I. What is the domain of ?
    III. What value is excluded from the denominator of all fractions?
    IV. Now combine these results to find the domain of .