Explanation:
The domain is the horizontal extent of the graph of the function. It is the set of all values of the independent variable for which the function is defined.
In a table or list of (x, y) or (x, f(x)) values the domain is the list of x-values.
On a graph, the domain is the horizontal extent of the graph, excluding any "holes" or vertical asymptotes. (The function is "undefined" at those places.)
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For a polynomial, the domain is generally "all real numbers."
For rational functions, the domain always excludes any x-values that make any denominator be zero.
For functions such as logarithms or roots, the domain is the set of values for which the function is defined. Even roots (square root, 4th root, ...) are only defined for non-negative numbers. Logarithms are only defined for positive numbers.
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In some problems, a model is often used that is defined for all values of the independent variable. For example, a height function may be modeled using a quadratic: h(t) = -4.9t^2 +30t +6. This is defined for all values of t, but the "practical domain" is the set of values of t ≥ 0 and before h(t) = 0. That is, we don't care about negative time or negative height.
