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The image outlines the following task for creating and analyzing a rational function:

1. **Create your own rational function**. (5 points)
2. **Find its domain (x)**. (5 points)
3. **Make a table of values**, choosing your own five (5) values for a domain (x). (5 points)
4. **Find the range (f(x) or y)** of your chosen domain. (5 points)

### To complete this:

1. **Step 1 (Create your own rational function)**:
   A rational function is of the form \( f(x) = \frac{P(x)}{Q(x)} \), where both \( P(x) \) and \( Q(x) \) are polynomials, and \( Q(x) \neq 0 \). An example of a simple rational function could be:
   \[
   f(x) = \frac{x^2 - 1}{x - 2}
   \]
   You can adjust this to suit your needs by modifying the polynomials in the numerator or denominator.

2. **Step 2 (Find its domain)**:
   The domain of a rational function is all real numbers except those that make the denominator \( Q(x) \) equal to zero. For the example above, we solve for \( x \) where:
   \[
   x - 2 = 0 \quad \Rightarrow \quad x = 2
   \]
   So, the domain is all real numbers except \( x = 2 \), i.e., \( x \in (-\infty, 2) \cup (2, \infty) \).

3. **Step 3 (Table of values)**:
   You would then choose five values for \( x \) from the domain and substitute them into the function to calculate the corresponding \( f(x) \) values. For example:
   - If \( x = 0 \), \( f(0) = \frac{0^2 - 1}{0 - 2} = \frac{-1}{-2} = 0.5 \)
   - Similarly, compute for other values of \( x \) such as \( -1 \), \( 1 \), \( 3 \), and \( 4 \).

4. **Step 4 (Find the range)**:
   After computing the table of values, the range would be the set of the calculated \( f(x) \) values for your chosen \( x \)-values.

Would you like to proceed with a specific function, or should I help you choose the \( x \)-values?

### Follow-up questions:
1. Do you have a specific rational function in mind, or would you like more examples?
2. How would you like to approach the domain restriction (e.g., more complex cases)?
3. Should we work through a specific set of \( x \)-values for the table of values?
4. Do you need clarification on finding the range of the function?
5. Would you like to explore more properties of rational functions, like asymptotes?

### Tip:
Always check where the denominator equals zero, as that helps determine restrictions in the domain of rational functions.

As a continuation of your previous lessons about rational functions, you will create your own rational function by following these steps: 1. Make your own rational function. 2. Find its domain (x). 3. Make a table of values choosing your own five values for a domain (x). 4. Find the range f(x) or y of your chosen domain.

Learn how to create a rational function, determine its domain, generate a table of values, and find the range. This guide covers rational functions, domains, and ranges for students in Grades 9-12.

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