Question

On what interval is the function positive?

Answer 1

To determine on what interval a function is positive, we need to find the values of x for which the function outputs positive y-values.

Step-by-step explanation:

To determine on what interval a function is positive, we need to find the values of x for which the function outputs positive y-values.

For example, let's consider the sine function. The sine function oscillates between +1 and -1 every 2 radians. This means that the function is positive in the intervals where it takes values greater than 0, which are the intervals between successive peaks (maximum points) of the sine wave.

Therefore, the function is positive on the intervals (0, 2π), (4π, 6π), (8π, 10π), and so on.

Answer 2

Answer: (-∞,2)

Step-by-step explanation: 2 is not included in the interval since at x=2, the function crosses the x axis, meaning it is not positive, and instead 0.

All x values below 2 are positive.