Question

consider the function graphed at right. the function has a select an answer of at x = the function is increasing on the interval(s): the function is decreasing on the interval(s): question help: video message instructor post to forum

Explanation:

Step1: Identify the vertex

The graph is a parabola opening down - ward. The vertex of a parabola gives the maximum value. The vertex of the parabola is at the point where the function changes from increasing to decreasing. From the graph, the vertex is at $x=- 3$. The function has a maximum value at this point.

Step2: Determine increasing intervals

A function is increasing when the $y$ - values are getting larger as the $x$ - values increase. Looking at the graph, the function is increasing on the interval $(-\infty,-3)$.

Step3: Determine decreasing intervals

A function is decreasing when the $y$ - values are getting smaller as the $x$ - values increase. From the graph, the function is decreasing on the interval $(-3,\infty)$.

Answer:

The function has a maximum of at $x = - 3$.
The function is increasing on the interval(s): $(-\infty,-3)$.
The function is decreasing on the interval(s): $(-3,\infty)$.