can you check my answers please.

Use the Leading Coefficient Test to determine the end behavior of the polynomial function.

f(x) = 4x^4 + 5x^3 + 2x^2 + 4x - 3
i got that it rises to the left and rises to the right

f(x) = -5x^4 - 2x^3 - 4x^2 - 4x + 2
i got that it falls to the left and rises to the right

f(x) = 2x^3 - 3x^2 + 2x + 4
i got that it rises to the left and rises to the right

678

(3*+2x)*

To determine the end behavior of a polynomial function, you can follow these steps:

1. Identify the leading coefficient: The leading coefficient is the coefficient of the term with the highest degree.

2. Analyze the sign of the leading coefficient:
- If the leading coefficient is positive, the polynomial rises to the right (as x approaches positive infinity) and rises to the left (as x approaches negative infinity).
- If the leading coefficient is negative, the polynomial falls to the right (as x approaches positive infinity) and falls to the left (as x approaches negative infinity).

Now, let's check your answers:

1. f(x) = 4x^4 + 5x^3 + 2x^2 + 4x - 3
- The leading coefficient is 4, which is positive. Therefore, the function rises to the right and rises to the left.
- Your answer is correct.

2. f(x) = -5x^4 - 2x^3 - 4x^2 - 4x + 2
- The leading coefficient is -5, which is negative. Therefore, the function falls to the right and rises to the left.
- Your answer is correct.

3. f(x) = 2x^3 - 3x^2 + 2x + 4
- The leading coefficient is 2, which is positive. Therefore, the function rises to the right and rises to the left.
- Your answer is correct.

Based on the leading coefficient and your analysis, all of your answers are correct. Well done!