The following is a worksheet I used with my students as extra practice after discussing things that limit domains, such as square roots and denominators. Important ideas to discuss with students before doing this worksheet:

1. Denominators can't be equal to zero. Thus, if a denominator is (x - 1), we have x - 1 ≠ 0, or x ≠ 1
2. Since it's not possible to take the square root of a negative number, the contents of a radical can't be negative. Thus, if we have
   2x + 4
   , then 2x + 4 ≥ 0, or x ≥ -2.
3. n^th roots have the same restriction only if n is an even number. Thus, cube roots and fifth roots have no restrictions, while fourth roots do.
4. If the expression inside a radical contains exponents, factor the expression. Then determine in which regions of the real numbers the roduct of those factors is non-negative. For example, if you have (x - 3)(x + 2) >0, we have two points of interest: 3 and -2. If x < -2, both factors are negative, and if x > 3, both factors are positive, resulting in a positive product. Thus, x < -2 or x > 3.
5. The same concept works for more than two factors. It also works for combinations of multiplication and division. If the number of negative factors is even within a certain region, the product is non-negative.
6. Since domain restrictions eliminate values in the real numbers, each restriction is cummulative in effect; if one restriction eliminates a number or region, and another restriction eliminates other numbers or regions, the result is the intersection of the allowed regions.