Question

refer to the figure below for 8 - 9. 8. identify the intervals of the graph as increasing or decreasing. a.) x < -3 ______increasing ____decreasing b.) -3 < x < 1 ____increasing ____decreasing c.) 1 < x < 2 ____increasing ____decreasing d.) x > 2 ____increasing ______decreasing 9. on which interval is the graph from question 8 negative? circle the correct answer. a.) x < -3 c.) x > 2 b.) -5 < x < -1 d.) -1 < x < 2

Explanation:

Step1: Analyze increasing - decreasing intervals

For an increasing function, as \(x\) increases, \(y\) increases. For a decreasing function, as \(x\) increases, \(y\) decreases.

• For \(x < - 3\), as \(x\) increases (moves to the right), \(y\) increases. So it's increasing.
• For \(-3 < x < 1\), as \(x\) increases, \(y\) increases. So it's increasing.
• For \(1 < x < 2\), as \(x\) increases, \(y\) decreases. So it's decreasing.
• For \(x>2\), as \(x\) increases, \(y\) increases. So it's increasing.

Step2: Analyze where the graph is negative

The graph is negative when \(y < 0\). Looking at the graph, for \(-5 < x < - 1\), the \(y\) - values of the graph are below the \(x\) - axis (\(y<0\)).

Answer:

8.
A. Increasing
B. Increasing
C. Decreasing
D. Increasing

1. B. \(-5 < x < -1\)