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To determine which type of function best models the inverse of the given data, let's break down the question and data provided.

The table shows the following pairs of \((x, y)\):

\[
\begin{array}{c|c}
x & y \\
\hline
-2 & 8 \\
-1 & 5 \\
0 & 4 \\
1 & 5 \\
2 & 8 \\
\end{array}
\]

The task is to model the **inverse** of this data. The inverse implies that you switch the roles of \(x\) and \(y\), so the new pairs would be:

\[
\begin{array}{c|c}
y & x \\
\hline
8 & -2 \\
5 & -1 \\
4 & 0 \\
5 & 1 \\
8 & 2 \\
\end{array}
\]

Now, we need to determine which function type best models this inverse relationship:

1. **Quadratic**: A quadratic function follows the form \(y = ax^2 + bx + c\). This could model data that has symmetry, such as data that increases and decreases around a point.

2. **Linear**: A linear function follows the form \(y = mx + b\), representing a straight-line relationship.

3. **Square root**: This function generally follows the form \(y = \sqrt{x}\), and it’s often useful when dealing with inverse relationships.

4. **Exponential**: An exponential function follows the form \(y = ab^x\), showing rapid increase or decrease.

Given that the data has a symmetric nature (values of \(y = 8\) at both ends, and values of \(y = 5\) in the middle), this suggests a **quadratic function** might model the data best.

Thus, the correct answer is likely **A) quadratic**.

Would you like a more detailed explanation or have any further questions?

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Here are five related questions you might find useful:

1. How do you calculate the inverse of a quadratic function?
2. What are the key characteristics of a linear function?
3. How does an exponential function differ from a quadratic function in terms of graph shape?
4. What are some real-life applications of inverse functions?
5. How do you determine the equation of a quadratic function from data points?

**Tip**: When dealing with inverse functions, always remember to switch \(x\) and \(y\) values and check for symmetry or patterns in the new data set!

What type of function could best model the inverse of the data in the table?

Understand how to determine the best function type to model the inverse of a given data table, focusing on concepts like quadratic equations, linear, square root, and exponential functions. This problem is ideal for students in Grades 8-10.

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