use the graph to answer the following questions.\n(a) over which intervals is the function decreasing…

use the graph to answer the following questions.\n(a) over which intervals is the function decreasing? choose all that apply.\n□(-∞, -7)□(-5, -2)□(-5, 3)□(3, 6)□(6, 8)□(8, ∞)\n(b) at which x - values does the function have local minima? if there is more than one value, separate them with commas.\n\n(c) what is the sign of the functions leading coefficient?\nselect\n\n(d) which of the following is a possibility for the degree of the function? choose all that apply.\n□4 □5 □6 □7 □8 □9

use the graph to answer the following questions.\n(a) over which intervals is the function decreasing? choose all that apply.\n□(-∞, -7)□(-5, -2)□(-5, 3)□(3, 6)□(6, 8)□(8, ∞)\n(b) at which x - values does the function have local minima? if there is more than one value, separate them with commas.\n\n(c) what is the sign of the functions leading coefficient?\nselect\n\n(d) which of the following is a possibility for the degree of the function? choose all that apply.\n□4 □5 □6 □7 □8 □9

Answer

Explanation:

Step1: Identify decreasing intervals

A function is decreasing when the graph goes down as we move from left - to - right. By observing the graph, we see it is decreasing on $(-\infty,-7)$ and $(3,6)$.

Step2: Find local minima

Local minima occur at points where the function changes from decreasing to increasing. From the graph, local minima occur at $x = - 7,3$.

Step3: Determine sign of leading coefficient

Since the graph has an even number of turning points and the ends of the graph go in the same (up - up) direction, the leading coefficient is positive.

Step4: Estimate degree of function

The number of turning points of a polynomial function is at most $n - 1$, where $n$ is the degree of the polynomial. The graph has 3 turning points. So the degree $n$ satisfies $n-1\geq3$, so $n\geq4$. Also, since the ends go in the same direction, the degree is even. So possible degrees are 4, 6, 8.

Answer:

(a) $(-\infty,-7),(3,6)$ (b) $-7,3$ (c) Positive (d) 4, 6, 8