Question

1. a) increasing: $(-\infty,0),(0.7,\infty)$ decreasing: $(0,0.7)$ b) increasing: $(-2,-1),(-1,0)$ decreasing: $(-\infty,-2),(0,\infty)$ c) increasing: $(-\infty,-0.7),(0,0.7)$ decreasing: $(-0.7,0),(0.7,\infty)$ d) increasing: $(-\infty,\infty)$ decreasing: no intervals exist.

Explanation:

Step1: Recall the definition of increasing and decreasing functions

A function \(y = f(x)\) is increasing on an interval \(I\) if for any \(x_1

Step2: Analyze the given graph

Looking at the graph of the function \(y = f(x)\), as \(x\) increases from \(-\infty\) to \(\infty\), the \(y\) - values of the function are always getting larger. That is, for any two points \(x_1\) and \(x_2\) such that \(x_1

So, the function is increasing on the interval \((-\infty,\infty)\) and there are no intervals on which it is decreasing.

Answer:

D. Increasing: \((-\infty, \infty)\) Decreasing: No intervals exist.