Question

describe the identified intervals below as increasing, decreasing, or constant.

Explanation:

Step1: Analyze the graph

For a function \( y = f(x) \), if as \( x \) increases, \( y \) also increases, the function is increasing. If as \( x \) increases, \( y \) decreases, the function is decreasing. If \( y \) does not change with \( x \), the function is constant.

Step2: Determine the intervals

Looking at the graph:

• In interval 1: As \( x \) increases (moving from left to right), \( y \) decreases. So it is a decreasing interval.
• In interval 2: As \( x \) increases, \( y \) decreases. So it is a decreasing interval.
• In interval 3: As \( x \) increases, \( y \) decreases. So it is a decreasing interval.
• In interval 4: As \( x \) increases, \( y \) is constant (horizontal line - like behavior in terms of no - change in \( y \) value for a range of \( x \) values). So it is a constant interval.
• In interval 5: As \( x \) increases, \( y \) decreases. So it is a decreasing interval.

Answer:

Interval 1: Decreasing, Interval 2: Decreasing, Interval 3: Decreasing, Interval 4: Constant, Interval 5: Decreasing.