The graph in the image shows a curve resembling a rational function with a vertical asymptote around $x = 1$ and behavior typical of a function like $y = \frac{1}{x-1}$.

From visual inspection:

1. Vertical Asymptote: The curve shoots upwards around $x = 1$, indicating a vertical asymptote at $x = 1$.
2. End Behavior: As $x$ moves further to the left, the curve approaches the x-axis, suggesting that as $x \to -\infty$, $y \to 0$. For positive $x$, the curve becomes negative as $x$ increases from 1 to 2.
3. Shape: The curve behaves similarly to a rational function where the numerator and denominator have a specific relationship, typically something like $y = \frac{A}{x - 1} + B$.

Likely Equation

Based on the graph, the function is most likely of the form:

$y = \frac{-1}{x - 1}$

This rational function accounts for the vertical asymptote at $x = 1$ and the behavior of the curve decreasing as $x$ increases from 1. The negative sign ensures the correct orientation of the curve.

Would you like a detailed step-by-step explanation on how this form was derived? Let me know!

Related Questions:

1. What is the effect of changing the numerator in a rational function?
2. How do vertical asymptotes affect the shape of a graph?
3. How would the graph change if the asymptote were at $x = 2$?
4. What happens when the degree of the polynomial in the numerator is greater than that of the denominator?
5. Can you describe how horizontal asymptotes influence the behavior of a function at extreme values of $x$?

Tip: For rational functions, the vertical asymptote occurs where the denominator equals zero, while the horizontal asymptote depends on the degree of the numerator and denominator.