Question

Select the correct answer.

This table models continuous function f.
x f(x)
-2 0
-1 -8
0
-6
0
1
2
3
4
0
If function f is a cubic polynomial, which statement most accurately describes the function over the interval (0, 1)?
O A.
OB.
O C.
O D.
The function is increasing over the interval (0, 1).
The function is constant over the interval (0, 1).
The function increases and decreases over the interval (0, 1).
The function is decreasing over the interval (0, 1).

Answer 1

The correct answer is B. The function is constant over the interval (0, 1).

We are given a table that models a continuous function f, which is a cubic polynomial. From the table, we can see that the function has a zero at x = -2 and a zero at x = 4. Since the function is continuous and is a cubic polynomial, it must also have a zero between x = -2 and x = 0, and another zero between x = 0 and x = 4.

We are asked to describe the function over the interval (0, 1). From the table, we can see that when x = 0.5, f(x) is equal to 0. Therefore, the function is constant over the interval (0, 1), since it takes the same value at both endpoints of the interval.

Therefore, the correct answer is B. The function is constant over the interval (0, 1).