Find the Domain y=10-x^2

Problem

y=10−x2

Solution

1. Identify the type of function. The given equation y=10−x2 is a polynomial function, specifically a quadratic function.

2. Determine any restrictions on the input variable x Polynomials do not contain divisions by zero, square roots of negative numbers, or logarithms of non-positive numbers.

3. Conclude that the function is defined for all real numbers because there are no mathematical operations that would result in an undefined value.

4. Express the domain in interval notation. Since x can be any real number, the domain extends from negative infinity to positive infinity.

Final Answer

Domain: *(−∞,∞)

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