Question

identify the interval(s) on which the function is decreasing.
a. (-3, -2)
b. (0, -2)
c. (-∞, -2)
d. (-∞, -3)

Explanation:

Step1: Recall the definition of a decreasing function

A function \(y = f(x)\) is decreasing on an interval if for any two points \(x_1\) and \(x_2\) in the interval with \(x_1

Step2: Analyze each option

• Option A: \((-3,-2)\)

This is a very small interval. Looking at the graph, we cannot say the function is decreasing over this entire interval.

• Option B: \((0, - 2)\)

Intervals are written with the smaller number on the left. So \((0,-2)\) is an incorrect interval notation.

• Option C: \((-\infty,-2)\)

If we take two points \(x_1

• Option D: \((-\infty,-3)\)

For any two points \(x_1

Answer:

D. \((-\infty,-3)\)