Question

9). identify the intervals where the following graph is increasing and decreasing.
increasing: ______
decreasing: ______

Explanation:

Step1: Recall increasing/decreasing definitions

A function is increasing on an interval if as \( x \) increases, \( y \) increases (graph rises from left to right). Decreasing if \( x \) increases, \( y \) decreases (graph falls from left to right).

Step2: Analyze the graph's slope

• From \( x = -6 \) (or the leftmost point) to \( x = 4 \): The graph rises (slope positive), so it's increasing here.
• From \( x = 4 \) to \( x = 6 \): The graph falls (slope negative), so it's decreasing here.

Answer:

Increasing: \( (-\infty, 4) \) (or from \( x = -6 \) to \( x = 4 \), considering the graph's visible domain)
Decreasing: \( (4, 6) \) (or from \( x = 4 \) to \( x = 6 \))