To find the range of the function from the graph, we need to look at the possible $y$-values the function takes as the $x$-values vary.

Analyzing the graph:

1. The function appears to decrease and approach negative infinity as $x$ approaches negative infinity.
2. There is a local maximum at $y = 7$ around $x = -5$, which is the highest point on the graph.
3. The function then decreases again after reaching that maximum but seems to stabilize around $y = 2$ as $x$ approaches positive infinity (where a solid point marks a boundary).

Range:

• The function covers all $y$-values from negative infinity up to $y = 7$, including the point at $y = 7$ (due to the smooth connection), but it never exceeds 7.
• This suggests the range of the function is: $(-\infty, 7]$

So, the correct answer for the range is $(-\infty, 7]$.

Would you like a further explanation or have additional questions?

5 Related Questions:

1. What is the domain of this function based on the graph?
2. How do you determine if a function is continuous from its graph?
3. What are the maximum and minimum values of the function?
4. How can you tell if the function is increasing or decreasing at specific intervals?
5. How does the horizontal asymptote affect the range of a function?

Tip:

When analyzing a graph, look for key features like maximum/minimum points and asymptotes to determine the range effectively.