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.