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The image shows a multiple-choice question related to interpreting a graph of a function. Here is the question and the options provided:

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**Question 4 of 21:**

**Using the graph to determine the maximum domain restriction for the following equation, where the solution (𝑦) can only be found using the points within the domain selected:**

\[ y = \frac{7x}{1 - x^2} \]

(A) **The interval \([-2, -1]\)**  (Use interval notation.)

(B) **The interval \([1, 2]\)**  (Use interval notation.)

(C) **Select the correct answer using a large solid dot to select the correct interval of choice.**

(D) **Select the correct choice below and fill in the answer box to complete your choice.**

**Type an interval. (Type an integer or a simplified fraction.)**

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**Steps to Approach the Problem:**

1. **Understand the Equation:** The function \( y = \frac{7x}{1 - x^2} \) can have restrictions based on the domain, which are points where the denominator becomes zero since division by zero is undefined.

2. **Analyze the Denominator:** The function becomes undefined when \( 1 - x^2 = 0 \). Solve this equation:
   
   \[
   1 - x^2 = 0 \implies x^2 = 1 \implies x = \pm 1
   \]

   Therefore, the function is undefined at \( x = 1 \) and \( x = -1 \).

3. **Check the Graph:** The graph provided should show where the function is defined and where it is not. We are looking for intervals that do not include \( x = 1 \) and \( x = -1 \).

4. **Choose the Interval:** Based on the graph, we need to select intervals where the function is defined and which do not include the points where the function is undefined. The correct answer would be an interval that lies outside or does not include \( x = 1 \) and \( x = -1 \).

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**Suggested Answer:** Based on the function and typical graphical representations, the intervals \( [-2, -1] \) or \( [1, 2] \) would avoid \( x = -1 \) and \( x = 1 \) respectively, as required. The correct interval to select should be \( [1, 2] \), as it lies within the positive domain, which is often preferred for such functions.

Would you like more details on this solution, or do you have any specific questions about the problem? Here are some related questions:

1. What are the implications of a function being undefined at certain points?
2. How do you determine the domain of a function algebraically?
3. How does graphing help in identifying the domain and range of a function?
4. What is interval notation and how is it used in expressing domain restrictions?
5. How does the behavior of the function \( \frac{1}{1 - x^2} \) compare to similar rational functions?

**Tip:** Always check where the denominator of a rational function equals zero, as these points will not be included in the domain of the function.

Using the graph to determine the maximum domain restriction for the following equation, where the solution (𝑦) can only be found using the points within the domain selected: y = 7x / (1 - x^2)

Learn how to determine the maximum domain restriction of the function y = 7x / (1 - x^2) by analyzing its graph. This problem helps you understand the domain and range of rational functions, with a focus on algebraic and graphical methods. Suitable for students in Grades 9-12.

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