https://file.aiquickdraw.com/mathbot/file/1726403791350xf72nkhq.jpg

Here is the graph of the exponential function \( y = 0.5^x \), along with the five selected points: (-2, 4), (-1, 2), (0, 1), (1, 0.5), and (2, 0.25). The graph illustrates an exponential decay, where the values decrease as x increases.

### Key Points:
- The **domain** is all real numbers \( (-\infty, \infty) \).
- The **range** is positive values \( (0, \infty) \), meaning \( y \) never reaches 0 but gets closer as \( x \) increases.

Would you like further details or clarifications on this topic? 

### Here are 5 related questions for further exploration:
1. How does changing the base of the exponential function (e.g., using 0.25 or 0.75) affect the graph?
2. What is the effect of a vertical shift (e.g., \( y = 0.5^x + 2 \)) on the graph and its range?
3. How does the graph of an exponential growth function (e.g., \( y = 2^x \)) compare with this decay function?
4. How do exponential functions apply in real-world situations like radioactive decay or population decline?
5. What happens to the graph if we reflect it over the x-axis (e.g., \( y = -0.5^x \))?

### Tip:
Exponential decay functions like \( y = 0.5^x \) are used in fields such as physics and finance, where they model situations like depreciation of value or decay processes over time.

1 example of exponential function, then graph, construct at least 5 x and y (domain and range) less than 1.

Explore an example of an exponential decay function with y = 0.5^x, graphing at least 5 points, and analyzing the domain and range. Understand how the values decrease as x increases. Suitable for students in Grades 9-11.

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