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Answer:
- restrictions exclude parts of the domain where the function is not defined. On a graph, they are holes, or vertical asymptotes.
- the denominator might be (x² -4)
- they are different in the same way that adding and multiplying numerical fractions are different
Explanation:
1. In general, restrictions on rational functions refer to values of the variable that make the denominator zero. The function will be undefined in that case. On a graph, such a location will show up as a "hole" or a vertical asymptote.
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2. If ±2 are excluded from the domain, we expect factors of (x-2)(x+2) in the denominator. That is, the denominator will have a factor of (x²-4). (There may be other factors that do not have real zeros.)
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3. A rational expression is a fraction the same as any other. The usual rules of addition, subtraction, multiplication, and division apply. For addition and subtraction, it can be useful to identify a common denominator. For multiplication and division, that is not so essential.