The first image shows a graph of an exponential function, and the second image provides multiple-choice answers for the domain and range of the function.

Analyzing the Graph

1. Domain: The graph extends infinitely in both directions along the x-axis. Therefore, the domain of this exponential function is all real numbers.

2. Range: The function is entirely below the x-axis (negative y-values) and approaches the x-axis asymptotically but never crosses it. Thus, the range is $y < 0$.

Correct Answer

From the options provided in the second image:

• The correct answer is: Domain: all real numbers, Range: {y | y < 0}

Would you like further clarification or have additional questions?

Related Questions

1. What defines the range of an exponential function like the one shown?
2. How do horizontal asymptotes affect the range of a function?
3. Why does the domain of exponential functions typically include all real numbers?
4. What changes in domain or range occur if the graph is reflected across the x-axis?
5. How does the base of the exponential function affect the graph's shape and asymptote?

Tip

Remember, the range of exponential functions often depends on whether the graph is shifted, reflected, or scaled. Look for horizontal asymptotes to determine the range.