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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 <

What is the range of the function y = ³√(x) + 8?

Understand how to find the range of the function y = ³√(x) + 8 by analyzing the properties of cube root functions. Learn key concepts related to graphing and transformations, suitable for students in Grades 9-11.

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