https://file.aiquickdraw.com/mathbot/file/1725740150893wqwyyj6j.jpg

The graph in the image represents an exponential decay function, where the curve starts high on the left and approaches zero as it moves to the right. This suggests that the base of the exponential function is a fraction less than 1. The possible answer choices are exponential functions.

Now, let's evaluate the answer choices:

1. \( y = 2 \left( \frac{1}{2} \right)^x \)
2. \( y = 2 \times 2^x \)
3. \( y = \left( \frac{1}{2} \right)^x \)
4. \( y = 2^x \)

Since the graph shows decay, meaning the function decreases as \( x \) increases, the base of the exponent must be less than 1. Thus, the choice must involve \( \left( \frac{1}{2} \right)^x \), which reflects this behavior.

The correct function corresponding to the graph is:

\[
y = \left( \frac{1}{2} \right)^x
\]

This is choice 3. It correctly models the exponential decay shown in the graph.

Would you like more details on this or have any other questions? Here are five follow-up questions for further practice:

1. How does the base of an exponential function affect its graph?
2. What happens if the base of an exponential function is greater than 1?
3. Can you explain why \( y = 2^x \) represents exponential growth?
4. What does it mean when an exponential function's base is between 0 and 1?
5. How would you graph \( y = \left( \frac{1}{2} \right)^x + 2 \)?

**Tip:** For any exponential function of the form \( y = a \left( \frac{1}{b} \right)^x \), when \( 0 < b < 1 \), the graph shows exponential decay.

Select the function of the given graph over the domain of -4 ≤ x ≤ 4. Based on the image, the graph represents exponential decay with answer choices provided.

Learn how to identify an exponential decay function from a graph. This problem focuses on the behavior of exponential functions with bases between 0 and 1, applying the concept of exponential decay over the domain of -4 ≤ x ≤ 4. Suitable for students in Grades 8-10.

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