Question

the domain of $y = x^3$ is
all real numbers.
$x > 0$.
$x \geq 0$.
done

Explanation:

To determine the domain of the function \( y = x^3 \), we analyze the nature of the function. The cube function \( f(x)=x^3 \) is a polynomial function. Polynomial functions (like linear, quadratic, cubic functions) are defined for all real numbers because we can substitute any real number for \( x \) and get a real - valued output. For example, if \( x = - 2 \), then \( y=(-2)^3=-8 \); if \( x = 0 \), then \( y = 0^3 = 0 \); if \( x = 3 \), then \( y=3^3 = 27 \). There are no restrictions such as division by zero (which is not present here) or taking the square root of a negative number (also not present here) that would limit the values of \( x \) we can use. So the domain of \( y=x^3 \) is all real numbers.

Answer:

all real numbers.