Answered

Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Experience the ease of finding accurate answers to your questions from a knowledgeable community of professionals. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

Select the correct answer.

This table models continuous function [tex]\( f \)[/tex].

[tex]\[
\begin{tabular}{|c|c|}
\hline
x & f(x) \\
\hline
-2 & 0 \\
\hline
-1 & -8 \\
\hline
0 & -6 \\
\hline
1 & 0 \\
\hline
2 & 4 \\
\hline
3 & 0 \\
\hline
\end{tabular}
\][/tex]

If function [tex]\( f \)[/tex] is a cubic polynomial, which statement most accurately describes the function over the interval [tex]\( (0,1) \)[/tex]?

A. The function is constant over the interval [tex]\( (0,1) \)[/tex]

B. The function is increasing over the interval [tex]\( (0,1) \)[/tex]

C. The function is decreasing over the interval [tex]\( (0,1) \)[/tex]

D. The function increases and decreases over the interval [tex]\( (0,1) \)[/tex]

Sagot :

GinnyAnswer
To determine the behavior of the function [tex]\(f\)[/tex] over the interval [tex]\((0, 1)\)[/tex] from the given data, we look at the values of the function at the endpoints of the interval:
- [tex]\( f(0) = -6 \)[/tex]
- [tex]\( f(1) = 0 \)[/tex]

We observe that [tex]\( f(x) \)[/tex] changes from [tex]\( -6 \)[/tex] at [tex]\( x = 0 \)[/tex] to [tex]\( 0 \)[/tex] at [tex]\( x = 1 \)[/tex].

Since [tex]\( f(1) > f(0) \)[/tex], we can conclude that the function [tex]\( f(x) \)[/tex] increases over this interval. Therefore, the behavior of [tex]\( f \)[/tex] over the interval [tex]\((0, 1)\)[/tex] is that it is increasing.

Thus, the correct answer is:

B. The function is increasing over the interval [tex]\((0, 1)\)[/tex].
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.