Question

use the graph to answer the following questions.
(a) over which intervals is the function increasing? choose all that apply.
(-\infty, - 5) (-5, -2) (-2, 2) (5, 8) (2, 8) (8, \infty)
(b) at which x - values does the function have local minima? if there is more than one value, separate them with commas.

(c) what is the sign of the functions leading coefficient?

Explanation:

Step1: Determine increasing intervals

A function is increasing when the graph goes up from left - to - right. From the graph, we can see the function 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. The x - values of local minima are x=-5 and x = 2.

Step3: Find sign of leading coefficient

Since the function has an even degree (ends in the same direction, both going up) and the right - hand end goes up, the leading coefficient is positive.

Answer:

(a) (-5, -2), (2, 8)
(b) - 5, 2
(c) Positive