Question

In the $xy$-plane, the graph of function $f$ has $x$-intercepts at $-3,-1,$ and $1$. Which of the following could define $f$?

• A. $f\left(x\right)=(x-3)(x-1)(x+1)$
• B. $f\left(x\right)=(x-3)(x-1{)}^2$
• C. $f\left(x\right)=(x-1)(x+1)(x+3)$
• D. $f\left(x\right)=(x+1{)}^2(x+3)$

Answer 1

The correct option is C $f\left(x\right)=(x-1)(x+1)(x+3)$

Since, $f\left(x\right)$ cuts $x$-axis at three different points $x=-3,x=-1,x=1$

$\therefore$ it has three factors $x+3,x+1,x-1$

$\therefore f\left(x\right)=(x-1)(x+1)(x+3)$

Option C is correct.