Question

describe the x-values for which the function is increasing, decreasing, positive, and negative. round values to the nearest hundredth.

the function is increasing when $x < \square$ and $x > \square$ and decreasing when $\square < x < \square$.
the function is positive when $\square < x < \square$ and $x > \square$, and negative when $x < \square$ and $\square < x < \square$.

Explanation:

Step1: Identify increasing intervals

From the graph, the function rises as \(x\) moves left from the local minimum, and rises as \(x\) moves right from the local maximum. The local minimum is at \(x \approx 1.15\), local maximum at \(x \approx -1.15\).
Increasing: \(x < -1.15\) and \(x > 1.15\)

Step2: Identify decreasing interval

The function falls between the local maximum and local minimum.
Decreasing: \(-1.15 < x < 1.15\)

Step3: Identify positive intervals

The function is above the x-axis (positive) between its left and middle x-intercepts, and right of its right x-intercept. The x-intercepts are \(x \approx -2.00\), \(x \approx 0.00\), \(x \approx 2.00\).
Positive: \(-2.00 < x < 0.00\) and \(x > 2.00\)

Step4: Identify negative intervals

The function is below the x-axis (negative) left of the first x-intercept, and between the middle and right x-intercepts.
Negative: \(x < -2.00\) and \(0.00 < x < 2.00\)

Answer:

The function is increasing when \(x < -1.15\) and \(x > 1.15\) and decreasing when \(-1.15 < x < 1.15\).
The function is positive when \(-2.00 < x < 0.00\) and \(x > 2.00\), and negative when \(x < -2.00\) and \(0.00 < x < 2.00\).