Determine the largest open intervals of the domain over which eac...

Question

Determine the largest open intervals of the domain over which each function is b) decreasing. See Example 9.

Accepted Answer

Hey, everyone here we are given that the graph shown has intervals at which it is increasing, decreasing and at which it is constant, we are asked to find the largest open interval of domain at which the function is decreasing. Here we have four answer choice options, answer choice A which is an interval from negative infinity to negative three answer choice B negative 320, answer choice C negative infinity 25 and answer choice D 02, positive infinity. Now it can be observed that over the open interval from negative 3 to 0, we see that the Y values are decreasing. So we see that F of X sub one is greater than F of X sub two when we have X sub one is less than X sub two. And now we can note that there are several open, open intervals over which the function is decreasing, such as from negative three to negative two or from negative 1 to 0. But we see that the overall open interval is all the way from negative 3 to 0. So since negative 3 to 0 is the overall interval for which we see the Y values are decreasing. We know that the required largest open interval is from negative 3 to 0 where both terms are excluded and therefore closed by parentheses. With this interval, we are left with answer choice B again from negative 3 to 0 as our largest open interval. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

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Determine the largest open intervals of the domain over which each function is b) decreasing. See Example 9.

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