Question

In which interval is 1/b^2, (1 over b squared)?

Number line is to scale: -1 between I and II, C between II and III, 0 between III and IV, B between IV and V.
A. Interval I
B. Interval II
C. Interval III
D. Interval IV

Answer 1

The interval in which 1/b^2 lies is Interval IV.

Step-by-step explanation:

The expression 1/b^2 represents a quadratic function. To determine the interval in which this function lies, we need to evaluate its sign for different values of b.

If b < 0, then b^2 > 0 and 1/b^2 > 0. Therefore, the function is positive in Interval II.

If b = 0, then 1/b^2 is undefined.

If b > 0, then b^2 > 0 and 1/b^2 > 0. Therefore, the function is positive in Interval IV.

Based on the analysis above, the interval in which 1/b^2 is positive is Interval II and Interval IV. Therefore, the answer is Option D: Interval IV.