1. We want to find the range of the function $y = x^2$. 2. This means we want to know all the possible values $y$ can be when $x$ is any number. 3. When you square a number (multiply it by itself), the answer is never negative. 4. The smallest value you can get is 0, which happens when $x = 0$. 5. If you pick bigger or smaller numbers for $x$, the value of $y$ gets bigger and bigger. 6. So, $y$ can be 0 or any number bigger than 0. Final answer: The range of $y = x^2$ is all numbers $y$ such that $y \geq 0$, or simply $[0, \infty)$.