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.