Let's analyze the function given in the problem:

$y = \sqrt[3]{x} + 8$

Step 1: Understanding the Cube Root Function

The cube root function, $y = \sqrt[3]{x}$, has a domain and range of all real numbers:

$(-\infty, \infty)$

Since cube roots are defined for all real values of $x$, adding 8 simply shifts the function vertically by 8 units. This does not affect the range—it remains all real numbers.

Step 2: Identifying the Correct Answer

From the multiple-choice options:

• $-\infty < y < \infty$ ✅ (Correct)
• $-8 < y < \infty$ ❌ (Incorrect, since $y$ can take any negative value)
• **( 0 \leq y <