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 . (simplify your answer. type an integer or a fraction. use a comma to separate answers as needed. type each answer only once.)

Explanation:

Step1: Find x - intercepts

Set \(f(x)=0\), so \((x + 1)(x - 3)(x+4)=0\). By the zero - product property, if \(ab = 0\), then \(a = 0\) or \(b = 0\). So \(x+1=0\) gives \(x=-1\), \(x - 3=0\) gives \(x = 3\), and \(x + 4=0\) gives \(x=-4\).

Step2: Find y - intercept

Set \(x = 0\) in \(f(x)\). Then \(f(0)=(0 + 1)(0 - 3)(0+4)=1\times(-3)\times4=-12\). But we are only asked for x - intercepts here.

Answer:

-1,3,-4