Question

graph the polynomial function f(x)=(x + 1)(x - 3)(x + 4) using parts (a) through (e). (a) determine the end behavior of the graph of the function. the graph of f behaves like y = x^3 for large values of |x|. (b) find the x - and y - intercepts of the graph of the function. the x - intercept(s) is/are - 1,3, - 4. (simplify your answer. type an integer or a fraction. use a comma to separate answers as needed. type each answer only once.) the y - intercept is . (simplify your answer. type an integer or a fraction.)

Explanation:

Step1: Recall y - intercept formula

To find the y - intercept, set \(x = 0\) in the function \(f(x)=(x + 1)(x - 3)(x + 4)\).

Step2: Substitute \(x = 0\)

\(f(0)=(0 + 1)(0 - 3)(0+4)\).

Step3: Calculate the product

\(f(0)=1\times(-3)\times4=-12\).

Answer:

\(-12\)