Question

consider the following polynomial function.
$f(x)=(x + 1)(x - 1)(x - 3)$
answer the questions regarding the graph of $f$.
then, use this information to graph the function.
(a) choose the end behavior of the graph of $f$.
choose one
falls to the left and rises to the right
rises to the left and falls to the right
(b) rises to the left and rises to the right
falls to the left and falls to the right

Explanation:

Step1: Find polynomial degree and leading coefficient

First, expand the leading terms: $(x)(x)(x) = x^3$. The degree is 3 (odd), leading coefficient is 1 (positive).

Step2: Apply end behavior rules

For odd degree, positive leading coefficient: as $x\to-\infty$, $f(x)\to-\infty$ (falls left); as $x\to+\infty$, $f(x)\to+\infty$ (rises right).

Answer:

Falls to the left and rises to the right