A table of values is given for $Y _ { 1 } = f ( x )$ ). Determine whether the intermediate value theorem guarantees
that the function has a zero on the given interval.
-$\mathrm{Y}_{1}=17 x^{4}-39 x^{3}+186 x^{2}+298 x+398 \quad[-2,-1]$
$\begin{array}{r|r}
\mathrm{X} & \mathrm{Y}_{1} \
\hline-4 & 9,030 \
-3 & 3,608 \
-2 & 1,130 \
-1 & 342 \
0 & 398 \
1 & 860 \
2 & 1,698 \
3 & 3,290 \
\hline \mathrm{X}=-4 &
\end{array}$

A) Yes
B) No

Question

A table of values is given for $Y _ { 1 } = f ( x )$ ). Determine whether the intermediate value theorem guarantees
that the function has a zero on the given interval.
-$\mathrm{Y}_{1}=17 x^{4}-39 x^{3}+186 x^{2}+298 x+398 \quad[-2,-1]$
$\begin{array}{r|r}
\mathrm{X} & \mathrm{Y}_{1} \
\hline-4 & 9,030 \
-3 & 3,608 \
-2 & 1,130 \
-1 & 342 \
0 & 398 \
1 & 860 \
2 & 1,698 \
3 & 3,290 \
\hline \mathrm{X}=-4 &
\end{array}$

A) Yes
B) No

Quizplus · Accepted Answer

The Intermediate Value Theorem requires that the function changes sign over the interval. Since $Y_1$ is positive at both $x = -2$ and $x = -1$, the theorem does not guarantee a zero in this interval.

A Table of Values Is Given For Y1=f(x)Y _ { 1 } = f ( x )Y1​=f(x)

A Table of Values Is Given For $Y _ { 1 } = f ( x )$