 find the degree, the leading term, the leading coefficient, the constant term and
the end behavior of the given polynomial.
 f(x) = 4 − x − 3x


Let's first write down the polynomial function properly:

\[ f(x) = 4 - x - 3x \]

This expression can be simplified as follows:

\[ f(x) = 4 - 4x \]

### Key elements of the polynomial:
1. **Degree**: The degree of a polynomial is the highest power of the variable \( x \). In this case, the highest power of \( x \) is 1 (since \( -4x \) is \( -4x^1 \)). Therefore, the degree is:
   \[
   \text{Degree} = 1
   \]

2. **Leading Term**: The leading term is the term with the highest power of \( x \). Here, the leading term is:
   \[
   \text{Leading Term} = -4x
   \]

3. **Leading Coefficient**: The leading coefficient is the coefficient of the leading term. Here, the coefficient of \( -4x \) is:
   \[
   \text{Leading Coefficient} = -4
   \]

4. **Constant Term**: The constant term is the term that does not contain any variables. In this case, the constant term is:
   \[
   \text{Constant Term} = 4
   \]

5. **End Behavior**: The end behavior of a polynomial depends on the degree and the leading coefficient:
   - For a degree 1 polynomial with a **negative** leading coefficient, the graph will fall to the right and rise to the left.

   Hence, the end behavior is:
   \[
   \text{As } x \to \infty, f(x) \to -\infty \quad \text{and} \quad \text{as } x \to -\infty, f(x) \to \infty
   \]

### Summary:
- Degree: 1
- Leading Term: \( -4x \)
- Leading Coefficient: \( -4 \)
- Constant Term: \( 4 \)
- End Behavior: Falls to the right, rises to the left.

Would you like further details on any of these aspects?

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Here are 5 related questions for further exploration:
1. What is the effect of the leading coefficient on the end behavior of a polynomial?
2. How would the degree change the shape of the graph in higher degree polynomials?
3. How can you factor simple polynomials like \( f(x) = 4 - 4x \)?
4. What is the difference between even-degree and odd-degree polynomial end behaviors?
5. How do transformations like shifting and stretching affect polynomial graphs?

**Tip:** Always check the highest degree and leading coefficient when determining the end behavior of a polynomial!

find the degree, the leading term, the leading coefficient, the constant term and the end behavior of the given polynomial. f(x) = 4 − x − 3x

Explore the polynomial f(x) = 4 − x − 3x. Learn how to determine the degree (1), leading term (-4x), leading coefficient (-4), constant term (4), and the end behavior of this linear polynomial. Suitable for students in Grades 8-10.

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