Let's determine the points on the graph for each piece of the function \( f(x) \).

### 1. **For \( x < -4 \)**:
The function is constant at \( f(x) = 6 \). This means for all \( x < -4 \), the y-value is 6.

- Example points: 
  - \( (-5, 6) \)
  - \( (-6, 6) \)
  - \( (-7, 6) \)

### 2. **For \( -4 \leq x < 4 \)**:
The function is \( f(x) = -10 + x^2 \). We can calculate specific points by plugging in values of \( x \) within this interval.

- Example points:
  - \( (-4, 6) \) since \( f(-4) = -10 + (-4)^2 = 6 \)
  - \( (-2, -6) \) since \( f(-2) = -10 + (-2)^2 = -10 + 4 = -6 \)
  - \( (0, -10) \) since \( f(0) = -10 + 0^2 = -10 \)
  - \( (2, -6) \) since \( f(2) = -10 + 2^2 = -10 + 4 = -6 \)
  - \( (3, -1) \) since \( f(3) = -10 + 3^2 = -10 + 9 = -1 \)

### 3. **For \( x \geq 4 \)**:
The function is \( f(x) = 2x - 2 \). We can calculate specific points by plugging in values of \( x \) within this interval.

- Example points:
  - \( (4, 6) \) since \( f(4) = 2(4) - 2 = 8 - 2 = 6 \)
  - \( (5, 8) \) since \( f(5) = 2(5) - 2 = 10 - 2 = 8 \)
  - \( (6, 10) \) since \( f(6) = 2(6) - 2 = 12 - 2 = 10 \)

### Summary of Points:
- **For \( x < -4 \)**: 
  - \( (-5, 6) \), \( (-6, 6) \), \( (-7, 6) \), ...
- **For \( -4 \leq x < 4 \)**:
  - \( (-4, 6) \), \( (-2, -6) \), \( (0, -10) \), \( (2, -6) \), \( (3, -1) \), ...
- **For \( x \geq 4 \)**:
  - \( (4, 6) \), \( (5, 8) \), \( (6, 10) \), ...

These points can be used to plot the graph of the function \( f(x) \).

Would you like to see a plot of these points? Or do you have any other questions? Here are some related questions:

1. How does the shape of the parabola change if you modify the quadratic equation?
2. What are the points of intersection between different parts of the piecewise function?
3. How would you determine the slope of the line for \( x \geq 4 \)?
4. What happens to the function’s graph if we shift it vertically?
5. How do you find the vertex of the parabola part of the function?

**Tip**: When plotting a piecewise function, always pay special attention to points where the function changes its expression.

Explore how to determine points on a graph for a piecewise function f(x), covering constant, quadratic, and linear functions in different intervals. Detailed examples include calculating specific points and plotting the function.

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