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The question asks to find the slope of the function \( f(x) \) at \( x = -1 \) using the given graph.

To solve this:

1. **Find the Tangent Line at \( x = -1 \):** The slope of the function at \( x = -1 \) corresponds to the slope of the tangent line at that point on the graph.

2. **Pick Two Points on the Tangent Line:** You can choose two distinct points on the tangent line and calculate the slope by using the slope formula:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]
   where \( (x_1, y_1) \) and \( (x_2, y_2) \) are the coordinates of the two points on the tangent.

### From the graph:
- The function has a smooth curve, and at \( x = -1 \), the tangent line seems to be decreasing.
- Estimate the coordinates of two points on the tangent line (you can use a visual estimate from the graph).

After estimating or calculating the slope, the answer can be given either as a simplified fraction or a decimal rounded to four decimal places.

Let me know if you need help plotting the points or estimating the slope! Would you like more details or a worked-out example?

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Here are 5 related questions for practice:
1. What is the geometric interpretation of the slope of a tangent line?
2. How can the derivative of a function at a point be interpreted as the slope of the tangent line?
3. What is the difference between secant and tangent lines in the context of slope?
4. How can you approximate the slope of a curve at a point if the graph is complex?
5. How can the equation of the tangent line at a point be found?

**Tip:** Always try to visually inspect the graph to get an idea of the slope's sign (positive or negative) before calculating!

Find the slope of f(x) at x = -1. The graph of f(x) is shown. Move the point on the curve to x = -1. Then plot two points on the tangent line. Finally, calculate the slope of f(x) at x = -1. Write your answer as a simplified fraction or rounded to 4 decimal places.

Learn how to calculate the slope of a function f(x) at x = -1 using the graph and the tangent line. This problem involves key calculus concepts, such as derivatives and tangent lines. The step-by-step solution includes using the slope formula to find the exact or approximate slope.

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