This graph represents an exponential function with an asymptote at $y = 0$ (the x-axis). The domain and range of the function are determined as follows:

• Domain: The set of all possible $x$-values for which the function is defined. Here, the graph extends indefinitely in both directions along the x-axis, so the domain is all real numbers:
  $\text{Domain: } (-\infty, \infty)$

• Range: The set of all possible $y$-values the function can take. The graph approaches $y = 0$ but never reaches or goes below it, so the range is:
  $\text{Range: } (0, \infty)$

The correct choice among the provided options is the second one:

• Domain: all real numbers
• Range: $\{ y \,|\, y > 0 \}$

Would you like further clarification or an explanation of why the graph's behavior results in this domain and range?

5 Follow-up Questions:

1. What is an exponential function, and why does it have this range?
2. How do we find the domain and range of more complex graphs?
3. Why does the graph approach $y = 0$ without touching it?
4. What are some real-life applications of exponential functions?
5. How does shifting the graph vertically or horizontally affect the domain and range?

Tip:

When analyzing a graph for its domain and range, always check for points where the function is undefined (e.g., division by zero or square roots of negative numbers).