Question

1. determine which intervals the graph is increasing. choose all that apply:

a $(-\infty,-2)$
b $(-2,2)$
c $(2,\infty)$
d $(-\infty,\infty)$

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 \(x_10\), the function is increasing over its entire domain.

Step2: Identify the type of the given graph

The given graph is a straight - line (linear) graph. The general form of a linear function is \(y=mx + b\). The slope \(m\) of the given line can be calculated using the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points on the line, say \((0,0)\) and \((1,1)\). Then \(m=\frac{1 - 0}{1 - 0}=1>0\).

Step3: Determine the interval of increase

Since the function is a linear function with a positive slope (\(m = 1>0\)), it is increasing for all real values of \(x\). The domain of a linear function \(y=mx + b\) (where \(m
eq0\)) is \((-\infty,\infty)\).

Answer:

D. \((-\infty,\infty)\)