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The image contains five function-related problems where you're asked to evaluate the given functions. I'll break down the problems and solve each one for you:

1. **f(x) = 2x² - 11 + 3x; x = 10**
   \[
   f(10) = 2(10)^2 - 11 + 3(10)
   \]
   \[
   f(10) = 2(100) - 11 + 30 = 200 - 11 + 30 = 219
   \]
   So, \( f(10) = 219 \).

2. **f(x) = 6x² + 4x; x = 2**
   \[
   f(2) = 6(2)^2 + 4(2)
   \]
   \[
   f(2) = 6(4) + 8 = 24 + 8 = 32
   \]
   So, \( f(2) = 32 \).

3. **F(x) = 3x² + 5x; x = 2**
   \[
   F(2) = 3(2)^2 + 5(2)
   \]
   \[
   F(2) = 3(4) + 10 = 12 + 10 = 22
   \]
   So, \( F(2) = 22 \).

4. **F(x) = 2k² + 5k + 1; k = (k + 2)**
   In this case, it seems like \( k \) itself is replaced with \( k + 2 \). Let's substitute:
   \[
   F(k + 2) = 2(k + 2)^2 + 5(k + 2) + 1
   \]
   Expand and simplify:
   \[
   F(k + 2) = 2(k^2 + 4k + 4) + 5(k + 2) + 1
   \]
   \[
   F(k + 2) = 2k^2 + 8k + 8 + 5k + 10 + 1
   \]
   \[
   F(k + 2) = 2k^2 + 13k + 19
   \]
   So, \( F(k + 2) = 2k^2 + 13k + 19 \).

5. **f(x) = x - 2|2x - 7|; x = 7**
   \[
   f(7) = 7 - 2|2(7) - 7|
   \]
   \[
   f(7) = 7 - 2|14 - 7| = 7 - 2|7| = 7 - 14 = -7
   \]
   So, \( f(7) = -7 \).

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Would you like any detailed explanations for these solutions or have further questions?

Here are five related questions you could explore:
1. What happens when the function contains higher degree terms like \( x^3 \)?
2. How do absolute values affect the behavior of a function?
3. Can you graph these functions to see their behavior visually?
4. What are some real-world applications of quadratic functions?
5. How does the substitution of variables, like in problem 4, work in more complex cases?

**Tip:** Always double-check your substitutions and calculations, especially when dealing with exponents and absolute values!

Evaluate the following functions: 
1. f(x) = 2x² - 11 + 3x; x = 10 
2. f(x) = 6x² + 4x; x = 2 
3. F(x) = 3x² + 5x; x = 2 
4. F(x) = 2k² + 5k + 1; k = (k + 2) 
5. f(x) = x - 2|2x - 7|; x = 7

This page provides a step-by-step solution for evaluating functions, including quadratic functions and absolute value expressions. Learn to solve problems like f(x) = 2x² - 11 + 3x and f(x) = x - 2|2x - 7|, suitable for students in Grades 8-10.

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