consider the function in the graph to the right. the function has a select an answer of at x = the function…

Answer:

1. The function has a maximum of 6.25 at $x=-3.5$.
2. The function is increasing on the interval(s): $(-\infty, - 3.5)$.
3. The function is decreasing on the interval(s): $(-3.5,\infty)$.
4. The domain of the function is: $(-\infty,\infty)$.
5. The range of the function is: $(-\infty,6.25]$.

Explanation:

Step1: Identify the vertex

The highest - point of the parabola is at $(-3.5,6.25)$, so it's a maximum.

Step2: Determine increasing interval

The function rises from negative infinity to $x = - 3.5$.

Step3: Determine decreasing interval

The function falls from $x=-3.5$ to positive infinity.

Step4: Find the domain

Since the graph extends horizontally without bound, domain is all real numbers.

Step5: Find the range

The maximum value is $y = 6.25$ and the function goes downwards, so range is $y\leq6.25$.