Let's break down the problem based on the provided graph.

(a) Vertical and Horizontal Asymptotes:

1. Vertical Asymptote: This is where the graph approaches a vertical line but never touches it. From the graph, it appears that the graph approaches the line $x = -2$, so: $\text{Vertical asymptote(s): } x = -2$

2. Horizontal Asymptote: The horizontal asymptote is the horizontal line that the graph approaches as $x$ goes to infinity. The graph seems to approach $y = 1$, so: $\text{Horizontal asymptote(s): } y = 1$

(b) X-intercepts and Y-intercepts:

• X-intercepts: The x-intercepts occur where the graph crosses the x-axis, i.e., where $y = 0$. The graph intersects the x-axis at $x = 1$, so: $\text{X-intercept(s): } x = 1$
• Y-intercepts: The y-intercept is where the graph crosses the y-axis, i.e., where $x = 0$. The graph intersects the y-axis at $y = -3$, so: $\text{Y-intercept(s): } y = -3$

(c) Domain and Range:

1. Domain: The domain of the function is all the values of $x$ for which the function is defined. The graph is undefined at $x = -2$ (due to the vertical asymptote), so the domain is all real numbers except $x = -2$. In interval notation: $\text{Domain: } (-\infty, -2) \cup (-2, \infty)$

2. Range: The range is the set of all possible values of $y$. The function approaches but never reaches $y = 1$ (due to the horizontal asymptote), so the range excludes $y = 1$. In interval notation: $\text{Range: } (-\infty, 1) \cup (1, \infty)$

Let me know if you need more details on any part of this explanation!

Here are 5 related questions:

1. How would the function change if the horizontal asymptote were at $y = 2$ instead of $y = 1$?
2. What happens to the domain if there is a "hole" in the graph?
3. Can a rational function have more than one vertical asymptote? Explain.
4. How would you find the equation of a rational function given its asymptotes and intercepts?
5. How does the graph of a rational function behave near an asymptote?

Tip: When finding intercepts, always set the other variable (x or y) to 0 in the equation of the function!