QuestionAnalyze the polynomial function $f(x)=-4(x+4)(x-3)^{3}$ using parts (a) through (h) below. (a) Determine the end behavior of the graph of the function.
The graph of $f$ behaves like $y=$ $\square$ for large values of $|x|$. (b) Find the $x$-and $y$-intercepts of the graph of the function.
The $x$-intercept(s) is/are $\square$ . (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(s) is/are $\square$ 1. (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.) (c) Determine the real 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 real zero(s) of $f$ is/are $\square$ (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.)
The lesser zero is a zero of multiplicity $\square$ , so the graph of $f(1)$ $\qquad$ the $x$-axis at $x=$ $\qquad$ . The greater zero is a zero of multiplicity $\square$ so the graph off (2) $\qquad$ the $x$-axis at $x=$ $\square$ . (d) Use a graphing utility to graph the function. The graphs are shown in the viewing window $X_{\min }=-10, X_{\max }=10, X_{s d l}=1$, $Y_{\min }=-2100, Y_{\max }=2100 Y_{\text {scl }}=210$. Choose the correct graph below. A. B. c. D.