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The task involves evaluating each given function at specified values of \( x \). Here are the functions and the values of \( x \) provided in the table: \(-2, -1, 0, 1, 2\).

Let's compute each function step-by-step:

1. **Function \( a(x) = 3 \)**:  
   Since this is a constant function, the value of \( y \) is always 3 regardless of \( x \).

   \[
   y = 3 \text{ for all values of } x.
   \]

2. **Function \( b(x) = 2x - 1 \)**:  
   We evaluate this for each value of \( x \).

   - For \( x = -2 \):  
     \( b(-2) = 2(-2) - 1 = -4 - 1 = -5 \).
   - For \( x = -1 \):  
     \( b(-1) = 2(-1) - 1 = -2 - 1 = -3 \).
   - For \( x = 0 \):  
     \( b(0) = 2(0) - 1 = 0 - 1 = -1 \).
   - For \( x = 1 \):  
     \( b(1) = 2(1) - 1 = 2 - 1 = 1 \).
   - For \( x = 2 \):  
     \( b(2) = 2(2) - 1 = 4 - 1 = 3 \).

3. **Function \( c(x) = x^2 + 2x + 1 \)**:  
   We evaluate this for each value of \( x \).

   - For \( x = -2 \):  
     \( c(-2) = (-2)^2 + 2(-2) + 1 = 4 - 4 + 1 = 1 \).
   - For \( x = -1 \):  
     \( c(-1) = (-1)^2 + 2(-1) + 1 = 1 - 2 + 1 = 0 \).
   - For \( x = 0 \):  
     \( c(0) = 0^2 + 2(0) + 1 = 0 + 0 + 1 = 1 \).
   - For \( x = 1 \):  
     \( c(1) = 1^2 + 2(1) + 1 = 1 + 2 + 1 = 4 \).
   - For \( x = 2 \):  
     \( c(2) = 2^2 + 2(2) + 1 = 4 + 4 + 1 = 9 \).

4. **Function \( d(x) = x^3 - 5 \)**:  
   We evaluate this for each value of \( x \).

   - For \( x = -2 \):  
     \( d(-2) = (-2)^3 - 5 = -8 - 5 = -13 \).
   - For \( x = -1 \):  
     \( d(-1) = (-1)^3 - 5 = -1 - 5 = -6 \).
   - For \( x = 0 \):  
     \( d(0) = 0^3 - 5 = 0 - 5 = -5 \).
   - For \( x = 1 \):  
     \( d(1) = 1^3 - 5 = 1 - 5 = -4 \).
   - For \( x = 2 \):  
     \( d(2) = 2^3 - 5 = 8 - 5 = 3 \).

5. **Function \( e(x) = | -x - 5 | \)**:  
   We evaluate this for each value of \( x \).

   - For \( x = -2 \):  
     \( e(-2) = | -(-2) - 5 | = | 2 - 5 | = | -3 | = 3 \).
   - For \( x = -1 \):  
     \( e(-1) = | -(-1) - 5 | = | 1 - 5 | = | -4 | = 4 \).
   - For \( x = 0 \):  
     \( e(0) = | -(0) - 5 | = | -5 | = 5 \).
   - For \( x = 1 \):  
     \( e(1) = | -(1) - 5 | = | -6 | = 6 \).
   - For \( x = 2 \):  
     \( e(2) = | -(2) - 5 | = | -7 | = 7 \).

Here's the complete table with all the values:

| \( x \) | -2 | -1 | 0 | 1 | 2 |
|---------|----|----|---|---|---|
| \( a(x) \) | 3 | 3 | 3 | 3 | 3 |
| \( b(x) \) | -5 | -3 | -1 | 1 | 3 |
| \( c(x) \) | 1 | 0 | 1 | 4 | 9 |
| \( d(x) \) | -13 | -6 | -5 | -4 | 3 |
| \( e(x) \) | 3 | 4 | 5 | 6 | 7 |

Would you like further details or explanations on any specific function?

### Related Questions:
1. What are the properties of each type of function (linear, quadratic, cubic, and absolute value)?
2. How does the behavior of each function change as \( x \) approaches positive or negative infinity?
3. Can you explain how to graph each function and interpret their shapes?
4. What are the domain and range of each function?
5. How do transformations affect the functions, such as shifts, reflections, or stretching?

### Tip:
To verify your function evaluations, substitute the \( x \) values into the functions step-by-step, ensuring all arithmetic operations are correctly followed.

Given the functions a(x) = 3, b(x) = 2x - 1, c(x) = x^2 + 2x + 1, d(x) = x^3 - 5, and e(x) = | -x - 5 |, evaluate them for the values of x = -2, -1, 0, 1, 2 and complete the table.

Learn how to evaluate linear, quadratic, cubic, and absolute value functions for different values of x. This step-by-step guide covers the evaluation of a(x) = 3, b(x) = 2x - 1, c(x) = x^2 + 2x + 1, d(x) = x^3 - 5, and e(x) = | -x - 5 | for values of x = -2, -1, 0, 1, 2. Suitable for students in Grades 8-10.

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