Question

graph the polynomial function f(x)=(x + 1)(x - 3)(x + 4) using parts (a) through (e). (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 - 12. (simplify your answer. type an integer or a fraction.) (c) determine the zeros of the function and their multiplicity. use this information to determine whether the graph crosses or touches the x - axis at each x - intercept. the zero(s) of f 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: Recall zero - definition

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

Step2: Apply 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 \(x=-4\).

Answer:

\(-1,3,-4\)