Use the graph to determine open intervals on which the function is increasing, decreasing, or constant.
A function is defined as the change in the output value with respect to the input where the output variable is dependent upon the input variable.
Answer: Using the graph, the open interval on which the function is increasing is (-∞, -2) U (2, ∞) and decreasing in (-2, 2) interval. Also, there is no interval where the function is constant.
Let's analyze the graph
Explanation:
Let's look into the graph given to understand the open intervals on which the function is increasing, decreasing, or constant.
From the above graph, we see that the function starting from negative infinity increases till point A(-2, 16), that is, the value of y-coordinate increases with an increase in x-coordinate value. The interval is represented as (-∞, -2)
From point A(-2,16), the function starts decreasing and continues moving towards point B(2,-16), that is, the value of y-coordinate decreases with an increase in x-coordinate value. The interval is represented as (-2, 2).
Further, from point B(2,-16) we see that the function starts increasing again moving towards infinity, that is, the value of y-coordinate increases with an increase in x-coordinate value. The interval is represented as (2, ∞).
Also, there is no interval where the function is constant.