Question

select the correct answer.
this table models continuous function $f$.

$x$

$f(x)$

----

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-2

0

-1

-8

0

-6

1

0

2

4

3

0

if function $f$ is a cubic polynomial, which statement most accurately describes the function over the interval $(0, 1)$?

a. the function increases and decreases over the interval $(0, 1)$.
b. the function is increasing over the interval $(0, 1)$.
c. the function is constant over the interval $(0, 1)$.
d. the function is decreasing over the interval $(0, 1)$.

Explanation:

Step1: Analyze interval (0,1) values

We know $f(0) = -6$ and $f(1) = 0$.

Step2: Compare endpoint function values

Since $-6 < 0$, $f(x)$ goes from a lower value to a higher value as $x$ increases from 0 to 1. For a continuous cubic polynomial, this means the function is increasing over this interval.

Answer:

B. The function is increasing over the interval (0, 1).