It appears that you have uploaded an image of a graph and a question related to the range of the function. Let me analyze the graph and provide a detailed explanation.

Analysis of the Graph:

• The curve appears to be a part of a hyperbola or logarithmic function decreasing from the top left of the graph.
• The graph begins at a high value on the y-axis and approaches the x-axis as it moves to the right but does not touch or cross the x-axis.

Interpretation:

The range of a function refers to the set of possible y-values (outputs) that the function can take.

Based on the visual dataIt appears that you have uploaded an image of a graph and a question related to the range of the function. Let me analyze the graph and provide a detailed explanation.

Analysis of the Graph:

• The curve appears to be a part of a hyperbola or logarithmic function decreasing from the top left of the graph.
• The graph begins at a high value on the y-axis and approaches the x-axis as it moves to the right but does not touch or cross the x-axis.

Interpretation:

The range of a function refers to the set of possible y-values (outputs) that the function can take.

Based on the visual

• As $x$ increases, the curve approaches, but never quite reaches, the x-axis (which is the line $y = 0$).
• The graph starts at a relatively high y-value and decreases without ever becoming negative or reaching zero.

Conclusion:

• The range of the function seems to be all positive real numbers excluding zero.
• Mathematically, this is written as: $(0, \infty)$.

Let me know if you would like more details, or if you have further questions!

Follow-Up Questions:

1. What is the domain of this function based on the graph?
2. Can this function have any vertical asymptotes?
3. What type of function might this be (e.g., exponential, logarithmic, hyperbolic)?
4. How would you describe the end behavior of the function?
5. How can you find the x-intercepts of this function from the graph?

Tip:

Always observe asymptotes when identifying the range of a function, as they give important clues about the behavior of the function at extreme values.