use the graph to answer the following questions. (a) over which intervals is the function increasing? choose…

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

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

Answer

Answer:

(a) (-5, -2), (2, 8) (b) -5, 2 (c) Positive (d) 5, 7, 9

Explanation:

Step1: Determine increasing intervals

A function is increasing when the graph goes up from left - to - right. By observing the graph, we see it is increasing on (-5, -2) and (2, 8).

Step2: Identify local minima

Local minima occur at points where the function changes from decreasing to increasing. From the graph, we can see local minima at x = - 5 and x = 2.

Step3: Find sign of leading coefficient

Since the function goes up on the far - right side (as x approaches positive infinity), the leading coefficient is positive.

Step4: Determine possible degrees

The number of local extrema (local maxima and minima) of a polynomial function is at most one less than the degree of the polynomial. Here we have 2 local minima and potentially some local maxima. A polynomial of odd degree has opposite end - behaviors. Since our function has opposite end - behaviors (down on the left and up on the right) and 2 local minima, possible odd degrees greater than 2 are 5, 7, 9.