https://file.aiquickdraw.com/mathbot/file/1728583270175qggm2v8w.jpg

Let's address both parts of the image you uploaded:

### 1. **End Behavior of the Function**:

The function given is \( f(x) = -3x^5 + 2x^3 - 7x + 2 \). To determine the end behavior, we focus on the term with the highest degree (the leading term), which is \( -3x^5 \).

- As \( x \to +\infty \), the term \( -3x^5 \) dominates and becomes very negative, so \( f(x) \to -\infty \).
- As \( x \to -\infty \), the term \( -3x^5 \) also becomes negative because \( (-x)^5 = -x^5 \), so \( f(x) \to +\infty \).

Thus, the end behavior is:
- \( f(x) \to -\infty \) as \( x \to +\infty \)
- \( f(x) \to +\infty \) as \( x \to -\infty \)

This corresponds to the second option in the list.

### 2. **Evaluating the Function**:

The second problem asks to evaluate the function \( f(x) = -2x^3 - 3x^2 + x \) at \( x = 2 \).

Substitute \( x = 2 \) into the function:
\[
f(2) = -2(2)^3 - 3(2)^2 + 2
\]
\[
f(2) = -2(8) - 3(4) + 2
\]
\[
f(2) = -16 - 12 + 2
\]
\[
f(2) = -26
\]

So, the value of the function at \( x = 2 \) is \( -26 \).

### Summary:
1. The correct end behavior is: \( f(x) \to +\infty \) as \( x \to -\infty \), and \( f(x) \to -\infty \) as \( x \to +\infty \).
2. The value of the function at \( x = 2 \) is \( -26 \).

Would you like more details on any of these steps or additional questions? Here are some related questions for practice:

1. What would the end behavior be for \( f(x) = 3x^4 + x^2 - 5 \)?
2. How does the degree and leading coefficient of a polynomial affect its end behavior?
3. If \( f(x) = -x^6 + 4x^3 - x \), what are the end behaviors as \( x \to \infty \) and \( x \to -\infty \)?
4. Evaluate \( f(x) = x^3 - 4x^2 + 7x - 5 \) at \( x = -1 \).
5. How do higher-degree terms in a polynomial influence its graph's shape?

### Tip:
When determining the end behavior of a polynomial, always focus on the leading term (the term with the highest degree) because it dominates as \( x \) grows large in either direction.

Describe the end behaviors of the graph of the function: f(x) = -3x^5 + 2x^3 - 7x + 2, and evaluate the function f(x) = -2x^3 - 3x^2 + x at x = 2.

Analyze the end behavior of the polynomial function f(x) = -3x^5 + 2x^3 - 7x + 2 by examining the leading term. Also, learn how to evaluate f(x) = -2x^3 - 3x^2 + x at x = 2 with step-by-step solutions, suitable for students in Grades 10-12.

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