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Let's go through each part of the problem based on the provided function \( f(x) = 2x^3 + 3x^2 + 3 \).

### Part (a)
To find the maximum number of turning points of a polynomial function, we use the fact that the maximum number of turning points for a polynomial of degree \( n \) is \( n - 1 \). Here, the function \( f(x) = 2x^3 + 3x^2 + 3 \) has a degree of 3.

- **Maximum number of turning points**: \( 3 - 1 = 2 \).

This matches the answer filled in on the worksheet.

### Part (b)
For part (b), you are asked to identify the correct graph of the function \( f(x) = 2x^3 + 3x^2 + 3 \) using the specified window settings. The correct graph should have the characteristics of a cubic function with up to 2 turning points, as discussed. 

- From the given options, **Option C** is marked as correct. This graph is consistent with the shape of a cubic polynomial and the expected number of turning points.

### Part (c)
The end behavior of a polynomial function is determined by its leading term. In this case, the leading term of \( f(x) = 2x^3 + 3x^2 + 3 \) is \( 2x^3 \).

- As \( x \to \infty \), \( f(x) \to \infty \).
- As \( x \to -\infty \), \( f(x) \to -\infty \).

Thus, the end behavior resembles the function \( y = 2x^3 \).

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Would you like further details on any part of this explanation? 

### Related Questions:
1. How can we determine the turning points of a cubic function algebraically?
2. Why does the degree of the polynomial dictate the maximum number of turning points?
3. How does the leading coefficient affect the end behavior of a polynomial function?
4. What would the end behavior be if the leading term was negative?
5. How can graphing utilities help verify turning points and end behavior of functions?

#### Tip:
For polynomials, always look at the highest-degree term to determine the end behavior. This term alone dictates how the graph behaves as \( x \) approaches positive or negative infinity.

Consider the function f(x) = 2x^3 + 3x^2 + 3. Complete parts (a) through (e).

Learn how to determine the maximum number of turning points and the end behavior of the cubic function f(x) = 2x^3 + 3x^2 + 3. This solution covers key polynomial concepts, including the calculation of turning points, end behavior analysis, and graph selection.

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