consider the function shown in the following graph. assume that the function is defined for all real…

consider the function shown in the following graph. assume that the function is defined for all real numbers. note: you can click on the graph to enlarge it. for both parts below, use interval notation to enter your answer. for what x values is the function increasing? for what x values is the function decreasing?

consider the function shown in the following graph. assume that the function is defined for all real numbers. note: you can click on the graph to enlarge it. for both parts below, use interval notation to enter your answer. for what x values is the function increasing? for what x values is the function decreasing?

Answer

Explanation:

Step1: Recall increasing - decreasing concept

A function (y = f(x)) is increasing when the slope of the tangent line is positive and decreasing when the slope of the tangent line is negative. On a graph, we can visually identify these intervals.

Step2: Identify increasing intervals

Looking at the graph, we see that the function is increasing when we move from left - to - right and the (y) - values are getting larger. If we assume the critical points (where the function changes from increasing to decreasing or vice - versa) are at (x=a) and (x = b) (from the graph), the increasing intervals are where the curve goes up.

Step3: Identify decreasing intervals

The function is decreasing when we move from left - to - right and the (y) - values are getting smaller.

Answer:

Let's assume from the graph that the function is increasing on the intervals ((-\infty,a)\cup(b,\infty)) and decreasing on the interval ((a,b)) (you need to determine the actual values of (a) and (b) by looking at the graph precisely. For example, if the critical points are (x=- 2) and (x = 2), the function is increasing on ((-\infty,-2)\cup(2,\infty)) and decreasing on ((-2,2))). Without the actual graph values, we leave the answer in general interval - notation form as above.