Help!! **End Behavior of Polynomial Functions**In this educational resource, we will determine the end behavior of the graph of several polynomial functions given their algebraic expressions. For each function, we focus on the leading term, as it primarily dictates the end behavior of the polynomial.**Instructions:**- Choose the correct end behavior of the graph for each polynomial function from the given options.### Function Analysis#### (a) \( f(x) = -5x^5 + 4x^4 + 2x^2 - 9 \)- **Options:** - Falls to the left and rises to the right - Rises to the left and falls to the right - Rises to the left and rises to the right - Falls to the left and falls to the right- **Analysis:** The leading term is \(-5x^5\). Since the degree is odd and the leading coefficient is negative, the graph falls to the left and rises to the right.- **Correct Answer:** Falls to the left and rises to the right#### (b) \( f(x) = -x^3 - 6x^2 - 3x - 7 \)- **Options:** - Falls to the left and rises to the right - Rises to the left and falls to the right - Rises to the left and rises to the right - Falls to the left and falls to the right- **Analysis:** The leading term is \(-x^3\). Since the degree is odd and the leading coefficient is negative, the graph falls to the left and rises to the right.- **Correct Answer:** Falls to the left and rises to the right#### (c) \( f(x) = 2x(x-1)^2(x+3) \)- **Options:** - Falls to the left and rises to the right - Rises to the left and falls to the right - Rises to the left and rises to the right - Falls to the left and falls to the right- **Analysis:** Expand and consider the leading term: \( 2x(x^2 - 2x + 1)(x+3) \). After multiplying, the highest degree term will be \( 2x^4 \). Since the degree is even and the leading coefficient is positive, the graph rises to

(a)rise to the left and falls to the right

Choose the end behavior of the graph of each polynomial function. 4 (a) f(x) = -5x² + 4x + 2x² - 9 3 2 (b) f(x) = -x²³ - 6x - 3x - 7 (c) f(x) = 2x (x - 1)²(x + 3) Falls to the left and rises to the right Rises to the left and falls to the right Rises to the left and rises to the right O Falls to the left and falls to the right O Falls to the left and rises to the right Rises to the left and falls to the right O Rises to the left and rises to the right Falls to the left and falls to the right Falls to the left and rises to the right O Rises to the left and falls to the right Rises to the left and rises to the right Falls to the left and falls to the right X ? O O