https://file.aiquickdraw.com/mathbot/file/17269023963360pw3m21z.jpg

The image shows a graph of an exponential function with a horizontal asymptote along the x-axis (the line \( y = 0 \)) and a downward slope, suggesting it is a decreasing exponential function. We are tasked with finding the **range** and the **domain** of this function and expressing them as inequalities.

### Domain:
The domain of an exponential function is typically all real numbers, as the function is defined for every value of \( x \).
\[
\text{Domain:} \quad (-\infty, \infty)
\]
This can be written in inequality form as:
\[
\boxed{x \in (-\infty, \infty)}
\]

### Range:
Since the graph does not go below the asymptote at \( y = 0 \) and moves downward from positive infinity, the range is all values less than 0.
\[
\text{Range:} \quad (-\infty, 0)
\]
In inequality form:
\[
\boxed{y < 0}
\]

Would you like further details or explanations?

Here are 5 related questions to explore:
1. What is the effect of the base of an exponential function on its growth or decay?
2. How do vertical shifts affect the range of an exponential function?
3. Can the domain of an exponential function ever be restricted?
4. How does the horizontal asymptote influence the function's range?
5. What transformations would shift the graph upwards or downwards?

**Tip:** When working with exponential functions, always identify the horizontal asymptote first, as it helps determine the range!

Find the range and the domain of the exponential function shown in the graph with a horizontal asymptote at y = 0.

This example shows how to find the range and domain of an exponential function with a horizontal asymptote at y = 0. Learn how to express the domain as all real numbers and the range as y < 0, using inequalities.

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