Question

determine all intervals on which the graph of ( f ) is decreasing.

Explanation:

Step1: Recall decreasing function definition

A function \( f(x) \) is decreasing on an interval if, as \( x \) increases, \( f(x) \) decreases (i.e., the graph falls from left to right).

Step2: Analyze the graph's slope

• Look at the left - most part: From the left, the graph first rises to a peak (around \( x=-4 \)), then falls from \( x = - 4 \) to \( x=-2 \) (since as \( x \) goes from -4 to -2, \( y \) - values decrease).
• Then, the graph rises until \( x = 6 \), and then falls from \( x = 6 \) to \( x = 9 \) (as \( x \) increases from 6 to 9, \( y \) - values decrease).

Step3: Identify intervals

• The first decreasing interval: When \( x \) is in \( (-4, - 2) \), the graph is decreasing.
• The second decreasing interval: When \( x \) is in \( (6, 9) \), the graph is decreasing.

Answer:

The function \( f \) is decreasing on the intervals \((-4, - 2)\) and \((6, 9)\)