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The domain is simply all the valid input values you can put into a function. Usually, these are your x-values. If putting a certain number into the function causes a mathematical error (like dividing by zero), that number is not in the domain.
The range is all the possible output values the function can give you after you plug in the domain values. Usually, these are your y-values or f(x). It describes how high or low the graph can go.
Domain: All real numbers (-∞, ∞). You can square any number.
Range: y ≥ 0 or [0, ∞). When you square a real number, the result is never negative.
Domain: x ≠ 0. We cannot divide by zero.
Range: y ≠ 0. The fraction 1/x can never equal 0.
Domain: x ≥ 0 or [0, ∞). We cannot take the square root of a negative number in real numbers.
Range: y ≥ 0 or [0, ∞). The principal square root is always non-negative.
The domain is the complete set of all possible input values (usually the x-values) for which the function is defined and produces a real output.
The range is the complete set of all possible output values (usually the y-values or f(x)) that a function can produce from its domain.
Interval notation uses brackets like [ and ] for included values, and parentheses like ( and ) for excluded values or infinity. For example, [0, ∞) means all numbers greater than or equal to 0.
The domain is all real numbers except x = 0, because dividing by zero is undefined.
Yes, many functions like basic linear functions (e.g., f(x) = x) or odd-degree polynomials have both a domain and range of all real numbers.