The function y = x² is a quadratic function that represents a parabola opening upwards. To determine the range, we need to understand how the output (y values) behaves as we vary the input (x values).
As x takes on any real number (positive, negative, or zero), the value of y will always be non-negative because squaring any real number yields a value that is either zero or positive. Therefore, y = 0 when x = 0, and as x becomes larger or more negative, y becomes larger and grows without bound.
In conclusion, the range of the function y = x² is all real numbers greater than or equal to zero. This can be expressed in interval notation as [0, ∞).