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The problem requires analyzing the slope of the given function to fill in the table with approximate \( x \)-values where the slope changes behavior (positive or negative).

### Step 1: Observing the graph
The slope is positive or negative based on the derivative of the function:
- A **positive slope** means the graph is increasing.
- A **negative slope** means the graph is decreasing.
- At critical points (where the slope is zero), the function transitions between increasing and decreasing.

### Step 2: Key observations from the graph:
- The graph starts with a **positive slope** before it reaches a **maximum turning point**.
- It then has a **negative slope** as it decreases toward a **minimum turning point**.
- Finally, it transitions back to a **positive slope** as it increases.

### Step 3: Estimating the \( x \)-values
From the graph:
1. **Positive until**: The slope is positive until approximately \( x = -1.5 \) (first turning point, a maximum).
2. **Negative from**: The slope becomes negative at \( x = -1.5 \) and continues until approximately \( x = 1 \) (second turning point, a minimum).
3. **Negative until**: The slope is negative until \( x = 1 \).
4. **Positive from**: The slope becomes positive again at \( x = 1 \) and continues onward.

### Completed Table:
| **Slope**       | **x value**  |
|------------------|-------------|
| Positive until   | \( x = -1.5 \) |
| Negative from    | \( x = -1.5 \) |
| Negative until   | \( x = 1 \)    |
| Positive from    | \( x = 1 \)    |

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Would you like further clarification on slopes or derivatives? Let me know!

Here are 5 related questions:
1. What is the derivative of a function, and how does it relate to slopes?
2. How do we classify critical points of a function using derivatives?
3. How can we approximate turning points of a graph visually?
4. What does the second derivative tell us about concavity and turning points?
5. How would you find the exact \( x \)-values where the slope changes using calculus?

**Tip**: Remember, critical points occur where the derivative equals zero or is undefined!

Approximate the x values where the slope of the function changes its behavior as positive or negative.

Learn to analyze slopes of a graph using derivatives by identifying critical points. Approximate the x-values where the slope changes its behavior from positive to negative and vice versa. This guide includes turning points, slope transitions, and key calculus concepts for Grades 10-12.

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