Question

analyzing a graph to determine key features
analyze the functions graph to determine which statement is true.
over the interval -2.5, 0.5, the local maximum is 2.
as the x - values go to positive infinity, the functions values go to negative infinity.
the function is decreasing over the interval (-1, 0.75).
the function is negative for the interval -2, 0.

Explanation:

Step1: Analyze local maximum

Check the interval $[-2.5,0.5]$. The highest - point in this interval on the graph has a $y$ - value of 2.

Step2: Analyze end - behavior

As $x\to+\infty$, the function's values go to $+\infty$, not $-\infty$.

Step3: Analyze decreasing interval

The function is increasing over the interval $(-1,0.75)$.

Step4: Analyze where function is negative

The function is positive on part of the interval $[-2,0]$.

Answer:

Over the interval $[-2.5,0.5]$, the local maximum is 2.