https://r2.erweima.ai/mathbot/image/1726085217280p8fmxlxy.jpg

The graph shown in the image represents the **rational parent function**, which is given by:

\[
f(x) = \frac{1}{x}
\]

From the graph, we can see that the function has a vertical asymptote at \( x = 0 \) and a horizontal asymptote at \( y = 0 \). This means that the function is undefined at \( x = 0 \) because division by zero is undefined.

### Domain of the function:
The domain is the set of all possible values of \( x \) for which the function is defined. In this case, the function is defined for all values of \( x \) **except** \( x = 0 \).

Thus, the domain is:

\[
\text{Domain}: (-\infty, 0) \cup (0, \infty)
\]

This means the function is defined for all real numbers except \( x = 0 \).

Would you like further details or clarification? 

Here are 5 related questions you might find useful:
1. What is the range of the rational parent function \( f(x) = \frac{1}{x} \)?
2. What happens to the function as \( x \to 0 \) from the left and right?
3. How do horizontal and vertical asymptotes impact the domain and range of a rational function?
4. How does the graph of \( f(x) = \frac{1}{x} \) change if the function is transformed, such as \( f(x) = \frac{1}{x-2} \)?
5. Can a rational function have more than one vertical asymptote?

**Tip**: When identifying the domain of a rational function, look for values of \( x \) that make the denominator zero, as these are the values where the function is undefined.

What is the domain of the rational parent function as shown in the graph?

Learn how to find the domain of the rational parent function f(x) = 1/x by identifying where the function is undefined due to a vertical asymptote. This topic covers rational functions and their domains, with a focus on asymptotes. Suitable for high school students in Grades 9-12.

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