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The image contains a table where each row lists a function \( f(x) \), a specific value for \( x \), and the corresponding evaluation of \( f(x) \). The task is to evaluate each function with the given \( x \) value. Let's go through each one.

1. **Function: \( f(x) = 2x + 3 \)**  
   - For \( x = 4 \):
     \[
     f(4) = 2(4) + 3 = 8 + 3 = 11
     \]
   - For \( x = a \):
     \[
     f(a) = 2a + 3
     \]
   - For \( x = a + b \):
     \[
     f(a + b) = 2(a + b) + 3 = 2a + 2b + 3
     \]

2. **Function: \( f(x) = -5x + 3 \)**  
   - For \( x = 0 \):
     \[
     f(0) = -5(0) + 3 = 0 + 3 = 3
     \]
   - For \( x = 2b \):
     \[
     f(2b) = -5(2b) + 3 = -10b + 3
     \]
   - For \( x = 4a - 3 \):
     \[
     f(4a - 3) = -5(4a - 3) + 3 = -20a + 15 + 3 = -20a + 18
     \]

3. **Function: \( f(x) = x^2 + 4 \)**  
   - For \( x = 3 \):
     \[
     f(3) = 3^2 + 4 = 9 + 4 = 13
     \]
   - For \( x = a - b \):
     \[
     f(a - b) = (a - b)^2 + 4 = a^2 - 2ab + b^2 + 4
     \]
   - For \( x = 3x - 2 \):
     \[
     f(3x - 2) = (3x - 2)^2 + 4 = 9x^2 - 12x + 4 + 4 = 9x^2 - 12x + 8
     \]

4. **Function: \( f(x) = \sqrt{x - 3} \)**  
   - For \( x = 5 \):
     \[
     f(5) = \sqrt{5 - 3} = \sqrt{2}
     \]
   - For \( x = 4b + 3 \):
     \[
     f(4b + 3) = \sqrt{4b + 3 - 3} = \sqrt{4b}
     \]
   - For \( x = 2b^2 + 3 \):
     \[
     f(2b^2 + 3) = \sqrt{2b^2 + 3 - 3} = \sqrt{2b^2}
     \]

5. **Function: \( f(x) = \frac{x^2 - 4}{x - 2} \)**  
   - For \( x = 3 \):
     \[
     f(3) = \frac{3^2 - 4}{3 - 2} = \frac{9 - 4}{1} = 5
     \]
   - For \( x = 0 \):
     \[
     f(0) = \frac{0^2 - 4}{0 - 2} = \frac{-4}{-2} = 2
     \]
   - For \( x = b + 2 \):
     \[
     f(b + 2) = \frac{(b + 2)^2 - 4}{b + 2 - 2} = \frac{b^2 + 4b + 4 - 4}{b} = \frac{b^2 + 4b}{b} = b + 4
     \]

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you determine if a function is undefined for a particular value of \( x \)?
2. Can you explain how the quadratic formula relates to the solutions of quadratic functions?
3. What are the conditions for a square root function to be defined for all real numbers?
4. How do you simplify rational expressions, especially when factoring is involved?
5. What are the general rules for combining like terms in algebraic expressions?

**Tip:** When working with square roots, always ensure that the expression inside the square root is non-negative to avoid dealing with imaginary numbers in real-valued functions.

Evaluate each of the following functions with the given domain.

This problem involves evaluating various algebraic functions for specific values of x. The functions include linear, quadratic, square root, and rational expressions. Suitable for students in Grades 8-10.

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