f(x) = x2^2 + 2
 from 
x = 1
 to 
x = 2.

 
Incorrect: Your answer is incorrect.

It looks like you're evaluating the function \( f(x) = x \cdot 2^2 + 2 \) from \( x = 1 \) to \( x = 2 \).

### Steps:
1. **Rewrite the function:**  
   \[
   f(x) = x \cdot 2^2 + 2 = x \cdot 4 + 2 = 4x + 2
   \]

2. **Evaluate at \( x = 1 \):**
   \[
   f(1) = 4(1) + 2 = 4 + 2 = 6
   \]

3. **Evaluate at \( x = 2 \):**
   \[
   f(2) = 4(2) + 2 = 8 + 2 = 10
   \]

### Therefore:
- \( f(1) = 6 \)
- \( f(2) = 10 \)

If you'd like further clarifications or details on the function evaluation, feel free to ask!

### Related Questions:
1. How would the function change if the coefficient of 2 was different?
2. What is the general form of linear functions like \( f(x) = 4x + 2 \)?
3. How would the result change if the interval were from \( x = 0 \) to \( x = 2 \)?
4. Can you calculate the average rate of change of \( f(x) \) over the interval \( [1, 2] \)?
5. How would \( f(x) \) behave for negative values of \( x \)?

**Tip:** Always simplify the constants before evaluating a function to avoid errors.

Learn how to evaluate the linear function f(x) = 4x + 2 from x = 1 to x = 2. This step-by-step solution is designed for students in Grades 6-8, covering essential algebraic concepts and linear function evaluation.

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