https://file.aiquickdraw.com/mathbot/file/1726320449714ry1giwoi.jpg

The graph in the image represents an exponential decay function, with a horizontal asymptote at \( y = -4 \). Let's find the **domain** and **range** based on the information in the graph:

### Domain:
The graph extends infinitely in both the positive and negative \( x \)-direction. This means that the domain includes all real numbers.

\[
\text{Domain: } (-\infty, \infty) \quad \text{or} \quad x \in \mathbb{R}
\]

### Range:
The graph approaches the horizontal asymptote \( y = -4 \), but it never touches or goes below it. The graph extends upwards without bound, so the \( y \)-values are greater than \( -4 \).

\[
\text{Range: } (-4, \infty) \quad \text{or} \quad y > -4
\]

Would you like more details or have any questions?

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Here are 5 related questions to expand on this:
1. How do we determine the asymptote of an exponential function?
2. What are the transformations applied to a basic exponential function based on this graph?
3. How can you rewrite this exponential function if we are given the base form?
4. How does the range of an exponential growth function differ from decay?
5. What impact does changing the asymptote have on the range of an exponential function?

**Tip:** In exponential decay functions, the horizontal asymptote represents the value the function approaches but never quite reaches.

Find the domain and range of the given exponential function graph.

Learn how to find the domain and range of an exponential decay function from its graph. This problem highlights key concepts such as horizontal asymptotes and the behavior of exponential functions. Suitable for high school students (Grades 9-12).

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