Question

On what intervals is the function decreasing? Indicate intervals on the x-axis using the Ray tool for intervals that extend to infinity and the Segment tool for bounded intervals. Graph a ray by selecting the endpoint followed by a point on the ray. Graph a segment by selecting an endpoint followed by the other endpoint.

Answer 1

( -6,-2 ) and ( 3,7 )

Explanation:

We are given the graph of function which is increasing in some parts and decreasing in other.

Now in x < -6, the function is increasing to reach the point ( -6,5 ).

Also, in interval ( -6,-2 ) the function is decreasing to reach the point ( -2,-7 ).

Further, in interval ( -2,3 ) the function is increasing to reach the point ( 3,6 ).

Then, in interval ( 3,7 ) the function is decreasing to reach the point ( 7,-5 ).

Finally, in x > 7, the function is increasing to infinity.

Hence, we see that the intervals where the function is decreasing are ( -6,-2 ) and ( 3,7 ).

Further, the ray AB and the line segment AC plotted in the graph can be seen in the figure below.