Question

given the function f(n)=(n - 1)(n + 3)(n - 5)
its f - intercept is
its n - intercepts are
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question 6
determine an equation for the pictured graph. write your answer in factored form and assume the leading coefficient is either 1 or - 1, you should be able to determine which is the case by looking at the graph.
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Explanation:

Step1: Find the $f$-intercept

Set $n = 0$ in $f(n)=(n - 1)(n + 3)(n - 5)$.
$f(0)=(0 - 1)(0+3)(0 - 5)=(-1)\times3\times(-5)=15$.

Step2: Find the $n$-intercepts

Set $f(n)=0$. Then $(n - 1)(n + 3)(n - 5)=0$.
By the zero - product property, $n-1 = 0$ or $n + 3=0$ or $n - 5=0$.
So $n=1$ or $n=-3$ or $n = 5$.

Answer:

$f$-intercept: $15$
$n$-intercepts: $1,-3,5$

(For Question 6, since the graph is not fully described with key points like $x$-intercepts etc., we can't solve it completely. If we assume we had all necessary information about the $x$-intercepts say $x_1,x_2,\cdots,x_k$ and the leading coefficient $a=\pm1$ based on end - behavior, the factored form of the polynomial would be $y=a(x - x_1)(x - x_2)\cdots(x - x_k)$)