describe over what interval the graph below is increasing:\na $(-\\infty,-1.2)$\nb $(-1.2,2.7)$\nc…

describe over what interval the graph below is increasing:\na $(-\\infty,-1.2)$\nb $(-1.2,2.7)$\nc $(2.7,\\infty)$\nd $(-2.1,1.7)$

describe over what interval the graph below is increasing:\na $(-\\infty,-1.2)$\nb $(-1.2,2.7)$\nc $(2.7,\\infty)$\nd $(-2.1,1.7)$

Answer

Explanation:

Step1: Recall the definition of an increasing function

A function (y = f(x)) is increasing on an interval if for any two points (x_1) and (x_2) in the interval with (x_1<x_2), we have (f(x_1)<f(x_2)). Graphically, the function has a positive slope.

Step2: Analyze the given graph

Looking at the graph, we observe the following:

  • For the interval ((-\infty,- 1.2)), the function has a negative slope (it is decreasing).
  • For the interval ((-1.2,2.7)), as (x) increases, (y) also increases. The function has a positive slope in this interval.
  • For the interval ((2.7,\infty)), the function has a negative slope (it is decreasing).

Answer:

B. ((-1.2,2.7))