Final answer:
To find the x-intercepts, set the function f(x) equal to zero and solve for x. The x-intercepts are x = -3, x = 1, and x = -1. To find the y-intercept, substitute x = 0 into the function.
Step-by-step explanation:
To find the x-intercepts of the function f(x) = (x + 3)2 (x -1) (x +1), we set f(x) equal to zero and solve for x. Therefore, (x + 3)2 (x -1) (x +1) = 0. This equation can be solved by factoring.
Using the Zero Product Property, we set each factor equal to zero and solve for x. x + 3 = 0, x - 1 = 0, and x + 1 = 0. Solving these equations, we find that the x-intercepts are x = -3, x = 1, and x = -1.
To find the y-intercept, we substitute x = 0 into the function f(x) = (x + 3)2 (x -1) (x +1). Therefore, f(0) = (0 + 3)2 (0 -1) (0 +1). Evaluating this expression, f(0) = 9(0)(1) = 0.