Question

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

Explanation:

Step1: Analyze the function \( y = x^3 \)

The function \( y = x^3 \) is a cubic function. For any real number \( x \) (positive, negative, or zero), when we cube it:

• If \( x \) is positive, \( x^3 \) is positive (e.g., \( 2^3 = 8 \)).
• If \( x \) is negative, \( x^3 \) is negative (e.g., \( (-2)^3=-8 \)).
• If \( x = 0 \), \( x^3 = 0 \).

Step2: Determine the range

The range of a function is the set of all possible output values (\( y \)-values). Since we can get any real number as a result of cubing a real number (positive, negative, or zero), the range of \( y=x^3 \) is all real numbers.

Answer:

all real numbers.