Question

consider the function graphed below. state your answers using interval notation with parentheses only (assume that the answer excludes the endpoints of each interval). a. the function is increasing on the interval(s): (-∞,-2 b. the function is decreasing on the interval(s): 2,∞) c. the function is neither decreasing nor increasing on the interval(s): -2,2 incorrect! we kindly recommend reviewing the using a graph to determine where a function is increasing, decreasing, or constant, or alternatively, you may discussion with mathgpt for a comprehensive explanation.

Explanation:

Step1: Recall increasing - function definition

A function is increasing when moving from left - to - right and the y - values are getting larger. Looking at the graph, as we move from left to right on the interval $(-\infty,-2)$, the y - values of the function are increasing.

Step2: Recall decreasing - function definition

A function is decreasing when moving from left - to - right and the y - values are getting smaller. From the graph, as we move from left to right on the interval $(2,\infty)$, the y - values of the function are decreasing.

Step3: Recall constant - function definition

A function is neither increasing nor decreasing (constant) when the y - values remain the same as we move from left to right. On the interval $(-2,2)$, the y - value of the function is constant.

Answer:

a. $(-\infty,-2)$
b. $(2,\infty)$
c. $(-2,2)$