Question

graph the polynomial function f(x)=x(3 - x)(7 - x) 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: Recall x - intercept definition

Set \(f(x)=0\), so \(x(3 - x)(7 - x)=0\).

Step2: Solve for x

Using the zero - product property, if \(ab = 0\), then \(a = 0\) or \(b = 0\).
For \(x=0\), the equation holds.
For \(3 - x=0\), we get \(x = 3\).
For \(7 - x=0\), we get \(x = 7\).

Answer:

0, 3, 7