Question

graph the polynomial function f(x)=(x - 1)(x + 4)^2 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, - 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: Find the y - intercept

Set \(x = 0\) in \(f(x)=(x - 1)(x + 4)^{2}\). Then \(f(0)=(0 - 1)(0+4)^{2}\).
First, calculate \((0 + 4)^{2}=16\), then \((0 - 1)\times16=- 16\).

Answer:

-16