https://file.aiquickdraw.com/mathbot/file/1726900836317o320daha.jpg

Based on the image provided, we have a graph of an exponential function with the following characteristics:

1. **Horizontal asymptote**: It is located at \( y = -3 \), indicated by the dashed line.
2. **Behavior**: The curve approaches this asymptote from below but never touches it, and the graph decreases as \( x \to \infty \).

Now, let's address the questions:

### (a) **Range**:
- The function never reaches \( y = -3 \), but it decreases without bound below that value. Hence, the range consists of all values **below** \( y = -3 \).
- This can be written as the inequality: 
  \[
  y < -3
  \]

### (b) **Domain**:
- The graph extends infinitely to the left and right without any breaks or restrictions. This means the domain is all real numbers.
- So, the domain is:
  \[
  \text{All reals} \quad (\mathbb{R})
  \]

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Would you like more details about exponential functions or their properties?

Here are 5 related questions:
1. How do you find the horizontal asymptote of an exponential function?
2. What are the key features of exponential decay?
3. How can we determine the range of other types of exponential functions?
4. Can exponential functions have vertical asymptotes?
5. What is the effect of vertical shifts on the range of a function?

**Tip**: Always check the horizontal asymptote when determining the range of exponential functions, as they approach but never reach this value.

The graph of an exponential function is shown in the figure below. Find the range and the domain.

Learn how to determine the domain and range of an exponential function with a horizontal asymptote at y = -3. This problem covers key concepts related to exponential functions, horizontal asymptotes, and inequalities. Suitable for students in Grades 9-12.

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