The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. For the function f(x) = 3x^2, we can analyze it as follows:
- Understanding the Function: This function is a quadratic function, where 3 is the coefficient of x squared. Quadratics are polynomial functions characterized by a curve (a parabola) that opens upwards or downwards. In this case, since the coefficient is positive (3), the parabola opens upwards.
- Determining the Domain: The expression 3x^2 involves a simple polynomial term. Polynomials are defined for all real numbers since there are no restrictions such as square roots of negative numbers or denominators that could equal zero. Thus, you can substitute any real number for x without leading to an undefined outcome.
- Conclusion: Therefore, the domain of the function f(x) = 3x^2 is all real numbers. In interval notation, this is expressed as:
Domain: (-∞, ∞)
In summary, you can think of the domain for f(x) = 3x^2 as limitless, allowing for every real number to be input into the function. This property contributes to the function’s utility and versatility in mathematics, making it useful in various applications.