Question

Use interval notation to write the interval(s) over which is increasing, decreasing, and

constant.

Answer 1

Increasing: (-∞, -3) ∪ (-2, 0)

Decreasing: (-3, -2) ∪ (0, 3)

Constant: [3, ∞)

Explanation:

To identify the intervals where a function is increasing, decreasing, or constant, we need to determine whether the slope is positive, negative, or zero within those intervals.

Increasing

A function is increasing when its slope is positive, meaning that as x increases, y also increases.

Decreasing

A function is decreasing when its slope is negative, meaning that as x increases, y decreases.

Constant

A function is constant when its slope is zero, resulting in a horizontal line.

From observation of the given graph, the intervals over which the function is increasing, decreasing or constant are:

• (-∞, -3) → increasing
• (-3, -2) → decreasing
• (-2, 0) → increasing
• (0, 3) → decreasing
• [3, ∞) → constant

Combining these intervals we get:

• Increasing: (-∞, -3) ∪ (-2, 0)
• Decreasing: (-3, -2) ∪ (0, 3)
• Constant: [3, ∞)