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The diagram shows two functions: the function \( f(x) \) represented by the dashed line and a related function represented by the solid line.

We can analyze the solid line and look for key characteristics that will help us find the equation of the related function:

1. **Turning Points**: 
   - At \( (-2, 5) \), the function has a maximum.
   - At \( (2, -1) \), the function has a minimum.

2. **Symmetry**: The graph seems to exhibit symmetry about the y-axis, suggesting this might be an even function or something related to \( f(x) \).

3. **General Form**: The shape of the solid line suggests it could be a cubic function or a combination of polynomial functions.

Given these properties, the general structure of the solid line seems to follow a cubic polynomial of the form:

\[
y = ax^3 + bx^2 + cx + d
\]

We can determine the constants \(a\), \(b\), \(c\), and \(d\) by plugging in some points from the graph (such as \( (-2, 5) \), \( (2, -1) \), and others) into the polynomial.

Would you like me to compute the exact equation for this function based on these points?

The diagram shows the graph of f(x) as a broken line and the graph of a related function as a solid line. Write down the equation of the related function.

Analyze a graph showing two related functions, one represented by a dashed line and the other by a solid line. Learn how to determine the equation of a cubic polynomial from its turning points and symmetry properties. Suitable for Grades 10-12.

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