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Find the domain and range of any function in interval notation
f(x) = 2x + 3
Domain
Range
The domain of a function is the set of all possible input values (x-values) for which the function is defined. The range is the set of all possible output values (y-values).
The domain is the complete set of possible input values (x-values) for a function. It includes all x-values where the function is mathematically defined and produces a real number output.
The range is the complete set of possible output values (y-values) that a function can produce. It depends on both the function's rule and its domain.
Division by zero is undefined in mathematics. For rational functions, any x-value that makes the denominator zero must be excluded from the domain.
Parentheses ( ) indicate the endpoint is NOT included (open interval), while brackets [ ] indicate the endpoint IS included (closed interval). For example, [2, 5) includes 2 but not 5.
No. Linear functions have domain (-∞, ∞), but rational functions exclude values where the denominator is zero, and logarithmic functions only accept positive inputs.
Find the vertex of the parabola. If it opens upward (a > 0), the range is [vertex-y, ∞). If it opens downward (a < 0), the range is (-∞, vertex-y].
The union symbol ∪ combines multiple intervals. For example, (-∞, 2) ∪ (2, ∞) represents all real numbers except 2.
The size of domain and range sets can differ. For example, f(x) = x² has domain (-∞, ∞) but range [0, ∞). The range is "smaller" because negative outputs are impossible.
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