Answer
$f(-3)$ and $f(-2)$ have opposite signs,
so f(x) has a real zero between $-3$ and $-2.$
Work Step by Step
The Intermediate Value Theorem for Polynomial Functions$:$
Let $f$ be a polynomial function with real coefficients.
If $f(a)$ and $f(b)$ have opposite signs,
then there is at least one value of $c$ between $a$ and $b$ for which $f(c)=0$.
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$a=-3,\quad f(a)=3(-3)^{3}-10(-3)+9$
$=-81+30+9=-42\quad$(negative)
$b=-2,\quad f(b)==3(-2)^{3}-10(-2)+9$
$=-24+20+9=5\quad$(positive)
$f(-3)$ and $f(-2)$ have opposite signs,
so f(x) has a real zero between $-3$ and $-2.$
