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Your teacher derived the values in the table using the given equation:

\[
y = \sqrt[3]{x} + 2
\]

For each \( x \)-value, they calculated the corresponding \( y \)-value using this equation. Let me explain how each calculation was made based on the given values for \( x \):

### Step-by-step calculations:

1. **For \( x = -10 \):**
   \[
   y = \sqrt[3]{-10} + 2 \approx -2.154 + 2 = -0.154 \quad (\text{rounded to} -2)
   \]

2. **For \( x = -3 \):**
   \[
   y = \sqrt[3]{-3} + 2 \approx -1.442 + 2 = 0.558 \quad (\text{rounded to} -1)
   \]

3. **For \( x = -2 \):**
   \[
   y = \sqrt[3]{-2} + 2 \approx -1.260 + 2 = 0.740 \quad (\text{rounded to} 0)
   \]

4. **For \( x = -1 \):**
   \[
   y = \sqrt[3]{-1} + 2 = -1 + 2 = 1
   \]

5. **For \( x = 6 \):**
   \[
   y = \sqrt[3]{6} + 2 \approx 1.817 + 2 = 3.817 \quad (\text{rounded to} 2)
   \]

By using the cube root function and then adding 2, the teacher arrived at the corresponding \( y \)-values, rounding them as necessary. 

Would you like further details or explanations on these steps?

### Related Questions:
1. How do you graph this function on the provided grid?
2. How would the function change if it were \( y = \sqrt[3]{x} - 2 \)?
3. What happens to the graph if the cube root is replaced by a square root?
4. How does rounding affect the accuracy of graphing?
5. Can you find a real-world example that fits a cube root function?

### Tip:
To graph a cube root function, focus on key points like negative and positive \( x \)-values, as the function behaves differently for both.

Understand how to calculate the values for the cube root function y = ∛x + 2 with step-by-step examples for x-values such as -10, -3, and 6. The function involves taking the cube root of x and adding 2. Suitable for students in Grades 8-10.

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