The graph appears to represent a function that has a vertical asymptote at $x = 0$ and a horizontal asymptote at $y = 2$. The function decreases without bound as $x \to 0^{-}$ (as it approaches negative infinity) and increases without bound as $x \to 0^{+}$ (approaching positive infinity). Additionally, for large values of $x$, the function tends to the value $y = 2$ but never quite reaches it.

Range Analysis:

• The function appears to cover all values of $y$, except $y = 2$, where the graph has a horizontal asymptote.
• As $x \to 0^{-}$, $y \to -\infty$.
• As $x \to 0^{+}$, $y \to +\infty$.
• For larger values of $x$, $y$ approaches 2 from above.

Thus, the range of the function is all real values except $y = 2$.

Range in interval notation:

$(-\infty, 2) \cup (2, \infty)$

Would you like a more detailed breakdown or further clarification?

Here are 5 related questions to expand this topic:

1. What is the domain of the function based on the graph?
2. How do we determine the equation of the horizontal asymptote?
3. Can the vertical asymptote be used to identify a function's type, such as rational or logarithmic?
4. How does a horizontal asymptote affect the end behavior of the function?
5. Could you explain the significance of the function's behavior as $x \to 0$?

Tip: When analyzing the range, always pay attention to asymptotes, as they indicate values the function will approach but never reach.