Question

For the given table of values for a polynomial function, where must the zeros of the function lie?

Answer 1

Answer:

A. Between 3.0 and 3.5 and between 4.0 and 4.5

Step-by-step explanation:

The zeroes of a function occur whenever a value of x returns zero. To predict where the zeroes lie, determine the interval(s) where the function crosses the x-axis. This occurs when either $f(x)$ goes from a negative value to a positive value or vice versa.

From $x=3.0$ and $x=3.5$, the y-values go from 4.0 (positive) to -0.2 (negative), respectively. Therefore, there must be a zero in this interval.

From $x=4.0$ and $x=4.5$, the y-values go from -0.8 (negative) to 0.1 (positive), respectively. Therefore, there must also be a zero in this interval.

Thus, the zeros of this function occur between 3.0 and 3.5 and between 4.0 and 4.5, leading to answer choice A.