The graph shows a rational function with the following features:

• A vertical asymptote at $x = -1$, where the function is undefined.
• A horizontal asymptote at $y = 1$, which the function approaches but never reaches.

Observing the range:

• For values of $y > 1$: The function increases unboundedly on the left and decreases unboundedly on the right as $x$ moves away from the vertical asymptote.
• For values of $y < 1$: The function decreases unboundedly to negative infinity as $x$ approaches the vertical asymptote.

Excluded Value:

The function does not equal $y = 1$, as the graph approaches the horizontal asymptote $y = 1$ but never reaches it.

Conclusion:

The range of this function is: $\boxed{(-\infty, 1) \cup (1, \infty)}$

Let me know if you'd like a deeper explanation!

Here are five related questions to deepen your understanding:

1. How do horizontal and vertical asymptotes affect the range of a rational function?
2. What steps are used to algebraically determine the asymptotes of a function?
3. Could the function ever equal $y = 1$ under different transformations? Why or why not?
4. How can you confirm the range of a rational function algebraically?
5. What happens to the range if the horizontal asymptote shifts vertically?

Tip: To identify the range of a function, pay close attention to horizontal asymptotes and whether there are restrictions for specific $y$-values.