consider the function graphed at right. the function has a select an answer of at (x =) the function is…

Explanation:

Step1: Identify the vertex

The graph is a parabola opening downwards. The vertex gives the maximum value of the function. From the graph, the vertex is at the point $(- 2,4)$. So the function has a maximum of $4$ at $x=-2$.

Step2: Determine increasing intervals

A function is increasing when the $y -$ values are getting larger as $x$ increases. Looking at the graph, the function is increasing on the interval $(-\infty,-2)$.

Step3: Determine decreasing intervals

A function is decreasing when the $y -$ values are getting smaller as $x$ increases. From the graph, the function is decreasing on the interval $(-2,\infty)$.

Answer:

The function has a maximum of $4$ at $x = - 2$. The function is increasing on the interval $(-\infty,-2)$. The function is decreasing on the interval $(-2,\infty)$.