1. The problem asks for the range of the function $g(x) = x^2$. 2. The function $g(x) = x^2$ is a quadratic function that squares any real number $x$. 3. Important rule: Squaring any real number results in a value that is always greater than or equal to zero because $x^2 \geq 0$ for all real $x$. 4. Therefore, the smallest value of $g(x)$ is 0, which occurs when $x=0$. 5. As $x$ moves away from zero in either positive or negative direction, $g(x)$ increases without bound. 6. Hence, the range of $g(x)$ is all real numbers $y$ such that $y \geq 0$. 7. Among the options given: - a. $x \leq 0$ is incorrect because the range is not negative. - b. $x = 0$ is incorrect because the function takes values greater than zero as well. - c. $x \geq 0$ is correct. - d. $x \neq 0$ is incorrect because zero is included in the range. Final answer: c. $x \geq 0$