Question

indicate which intervals are increasing, decreasing, or constant

(there is a graph here)

(then there are multiple - choice questions:)

(first set of options for an unshown question about increasing intervals:)
□ c. (6) □ d. (2)
□ e. (4) □ f. (5)
□ g. none of them

which intervals, if any, are decreasing? select all that apply
□ a. (5) □ b. (6)
□ c. (3) □ d. (2)
□ e. (4) □ f. (1)
□ g. none of them

which intervals, if any, are constant? select all that apply
□ a. (2) □ b. (3)
□ c. (4) □ d. (5)
□ e. (6) □ f. (1)
□ g. none of them

Explanation:

1. Intervals that are Decreasing

To determine decreasing intervals, we check where the function's \( y \)-value decreases as \( x \) increases (the graph moves downward from left to right).

• Interval (2): The graph falls from left to right here.
• Interval (6): The graph falls from left to right here.
• Other intervals: (1) is increasing, (3) is increasing, (4) is constant, (5) is increasing.

2. Intervals that are Constant

A constant interval has a horizontal graph (no change in \( y \)-value as \( x \) changes).

• Interval (4): The graph is horizontal here (same \( y \)-value for all \( x \) in this interval).
• Other intervals: (1), (2), (3), (5), (6) are not horizontal (they increase or decrease).

Final Answers

Decreasing Intervals:

B. (6), D. (2)

Constant Intervals:

C. (4)

Answer:

1. Intervals that are Decreasing

To determine decreasing intervals, we check where the function's \( y \)-value decreases as \( x \) increases (the graph moves downward from left to right).

• Interval (2): The graph falls from left to right here.
• Interval (6): The graph falls from left to right here.
• Other intervals: (1) is increasing, (3) is increasing, (4) is constant, (5) is increasing.

2. Intervals that are Constant

A constant interval has a horizontal graph (no change in \( y \)-value as \( x \) changes).

• Interval (4): The graph is horizontal here (same \( y \)-value for all \( x \) in this interval).
• Other intervals: (1), (2), (3), (5), (6) are not horizontal (they increase or decrease).

Final Answers

Decreasing Intervals:

B. (6), D. (2)

Constant Intervals:

C. (4)