Based on the image, you are asked to write an equation for the rational function graph shown. The graph includes important features such as vertical asymptotes at $x = -1$ and $x = 2$, and a y-intercept at $(0, 0.2)$. The function likely has the following form:

$y = \frac{A}{(x + 1)(x - 2)}$

Here’s why:

1. Vertical Asymptotes: The graph has vertical asymptotes at $x = -1$ and $x = 2$. This suggests the denominator includes factors of $(x + 1)$ and $(x - 2)$, because the function approaches infinity as $x$ gets close to these values.

2. Y-intercept at $(0, 0.2)$: At $x = 0$, the graph passes through $y = 0.2$. You can use this point to find the value of $A$ by substituting $x = 0$ and $y = 0.2$ into the equation:

$0.2 = \frac{A}{(0 + 1)(0 - 2)} \Rightarrow 0.2 = \frac{A}{-2} \Rightarrow A = -0.4$

Thus, the equation of the function is:

$y = \frac{-0.4}{(x + 1)(x - 2)}$

Would you like further details or have any questions about this? Here are five related questions to expand your understanding:

1. What are the characteristics of rational functions in terms of asymptotes and intercepts?
2. How can we identify horizontal asymptotes for rational functions?
3. What is the effect of different values of $A$ on the shape of the graph?
4. How do we find slant asymptotes in rational functions?
5. Can you determine end behavior from the degree of the numerator and denominator in rational functions?

Tip: To find vertical asymptotes, set the denominator equal to zero and solve for $x$.