Question

describe over what interval the graph below is increasing:
a $(-\infty,-1.2)$
b $(-1.2,2.7)$
c $(2.7,\infty)$
d $(-2.1,1.7)$

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

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. \((-1.2,2.7)\)