Question

x f(x) 3.0 4.0 3.5 -0.2 4.0 -0.8 4.5 0.1 5.0 0.6 5.5 0.7 For the given table of values for a polynomial function, where must the zeros of the function lie? A. between 3.0 and 3.5 and between 4.0 and 4.5 B. between 3.5 and 4.0 and between 4.0 and 4.5 C. between 4.0 and 4.5 and between 4.5 and 5.0 D. between 3 .5 and 4.0 and between 4.0 and 4.5 E. between 3 .5 and 4.0 and between 5.0 and 5.5

Answer 1

A. between 3.0 and 3.5 and between 4.0 and 4.5

Explanation:

Answer 2

A. between 3.0 and 3.5 and between 4.0 and 4.5

Explanation:

The idea here is that if a function is continuous and you have points on opposite sides of the x-axis, then there must be a zero-crossing between those points. As the table and graph show, ...

... (3.0, 4.0) and (3.5, -0.2)

are points on opposite sides of the x-axis. So, there must be a zero crossing between x=3.0 and x=3.5.

Likewise, ...

... (4.0, -0.8) and (4.5, 0.1)

are points on opposite sides of the x-axis. So, there must be a zero-crossing between x=4.0 and x=4.5

The appropriate answer choice lists both of these possible zero crossings.