Question

question 3 of 4 (1 point) | question attempt: 3 of unlimited
$f(x)=(x + 1)(x - 1)(x - 3)$
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 $f$.
falls to the left and rises to the right
(b) list each real zero of $f$ according to the behavior of the graph at the $x$-axis near that zero. if there is more than one answer, separate them with commas. if there is no answer, click on
one\.
zero(s) where the graph crosses the $x$-axis:
zero(s) where the graph touches, but does not cross the $x$-axis:
(c) find the $y$-intercept of the graph of $f$.
y-intercept:

Explanation:

Step1: Analyze end behavior

The function $f(x)=(x+1)(x-1)(x-3)$ is a cubic (degree 3) polynomial with a positive leading coefficient. For odd-degree polynomials with positive leading coefficients, the graph falls left, rises right.

Step2: Find real zeros and behavior

Set $f(x)=0$, solve $(x+1)(x-1)(x-3)=0$. Each zero has multiplicity 1 (odd), so the graph crosses the x-axis at each zero.
Zeros: $x=-1, x=1, x=3$

Step3: Calculate y-intercept

Substitute $x=0$ into $f(x)$:
$f(0)=(0+1)(0-1)(0-3)=(1)(-1)(-3)=3$

Answer:

(a) Falls to the left and rises to the right
(b) Zero(s) where the graph crosses the x-axis: $-1, 1, 3$
Zero(s) where the graph touches, but does not cross the x-axis: None
(c) y-intercept: $3$