To determine the domain of the equation y = x² + 6x + 1, we need to consider the values of x that can be used without resulting in undefined expressions.
This is a polynomial equation, specifically a quadratic equation, where the highest power of x is 2. Quadratic functions are defined for all real numbers, meaning they do not have any restrictions or limitations based on the values of x.
Thus, the domain of the function can be expressed in two common ways:
- In interval notation, the domain is (−∞, +∞).
- In set-builder notation, the domain can be expressed as {x | x ∈ ℝ}, meaning all x that are real numbers.
In summary, the domain of the equation y = x² + 6x + 1 is all real numbers, (−∞, +∞).