To solve this problem, we need to analyze the given graph of the rational function $f(x)$. Let's look at the key features of the graph, such as asymptotes and intercepts, and determine their values:

1. Vertical Asymptote(s):

Vertical asymptotes occur where the function is undefined, usually when the denominator of the rational function equals zero. From the graph:

• The vertical asymptote is at $x = 2$.

2. Horizontal Asymptote(s):

Horizontal asymptotes indicate the behavior of the function as $x$ approaches $\infty$ or $-\infty$. From the graph:

• The horizontal asymptote is at $y = 0$.

3. X-Intercept(s):

The x-intercepts are the points where the graph crosses the x-axis (where $f(x) = 0$). From the graph:

• The graph does not intersect the x-axis, so there are no x-intercepts.

4. Y-Intercept:

The y-intercept is where the graph crosses the y-axis (where $x = 0$). From the graph:

• The y-intercept appears to be around $y = -0.5$.

Summary:

• Vertical Asymptote: $x = 2$
• Horizontal Asymptote: $y = 0$
• X-Intercepts: None
• Y-Intercept: $y = -0.5$

Would you like more details on each step or have any questions?

Related Questions:

1. What is a rational function, and how is it defined?
2. How can you find vertical asymptotes from the function's equation?
3. How do you determine horizontal asymptotes for different types of rational functions?
4. What are the conditions for a rational function to have a hole?
5. How do you find the x-intercepts algebraically for a given rational function?

Tip:

When analyzing a graph, always check for key points like intercepts and asymptotes to understand the function's behavior better.