Question

The function f(x) = |2x| - 15. Determine the open intervals over which the function has the following specified properties:

Increasing: Find the intervals where f(x) is increasing.
Decreasing: Find the intervals where f(x) is decreasing.

Answer 1

The function f(x) = |2x| - 15 is decreasing on the interval (-∞, 0) and increasing on the interval [0, +∞).

Step-by-step explanation:

The function f(x) = |2x| - 15 can be separated into two intervals: x < 0 and x ≥ 0. On the interval x < 0, the absolute value function |2x| is decreasing, so f(x) is also decreasing. On the interval x ≥ 0, the absolute value function |2x| is increasing, so f(x) is increasing.

Therefore, the function f(x) is decreasing on the interval (-∞, 0) and increasing on the interval [0, +∞).