Answer:
- ∞ < x < - 5 which in interval notation is (- ∞, - 5) → Positive Interval
- 5 < x < - 3 which in interval notation is (- 5, - 3) → Negative Interval
- 3 < x < 6 which in interval notation is (-3, 6) → Positive Interval
6 < x < ∞ which in interval notation is (6, ∞ ) → Positive Interval
Step-by-step explanation:
The intervals are the bounds defining the x values between consecutive zeros.
The polynomial will always have the same sign between consecutive zeros.
If the value of the polynomial in an interval is > 0 then it is a positive interval which means the graph is above the x-axis
If the value of the polynomial in an interval is < 0 then it is a negative interval which means the graph is below the x-axis
Looking at the graph we can see there are three zeros and therefore four intervals as follows
- ∞ < x < - 5 which in interval notation is (- ∞, - 5) → Positive Interval
- 5 < x < - 3 which in interval notation is (- 5, - 3) → Negative Interval
- 3 < x < 6 which in interval notation is (-3, 6) → Positive Interval
6 < x < ∞ which in interval notation is (6, ∞ ) → Positive Interval
