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!