Question

1. a) increasing: $(-\infty,-1.4),(0,1.4)$ decreasing: $(-1.4,0),(1.4,\infty)$ b) increasing: $(-1,\infty)$ decreasing: $(-\infty,-1)$ c) increasing: $(-1,0),(1,\infty)$ decreasing: $(-\infty,-1),(0,1)$ d) increasing: $(-\infty,-4)$ decreasing: $(-4,\infty)$

Explanation:

Step1: Recall function increasing/decreasing definition

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

Step2: Analyze the graph

• Look at the left - hand side of the graph. As \(x\) moves from \(-\infty\) to \(-1.4\), the \(y\) - values of the function are increasing.
• As \(x\) moves from \(-1.4\) to \(0\), the \(y\) - values of the function are decreasing.
• As \(x\) moves from \(0\) to \(1.4\), the \(y\) - values of the function are increasing.
• As \(x\) moves from \(1.4\) to \(\infty\), the \(y\) - values of the function are decreasing.

Option B is incorrect because the behavior of the function is not based on \(x=-1\). Option C is incorrect as the intervals \((-1,0)\) and \((1,\infty)\) for increasing and \((-\infty,-1)\) and \((0,1)\) for decreasing do not match the graph. Option D is incorrect since the critical points are not at \(x = - 4\).

Answer:

A. Increasing: \((-\infty,-1.4),(0,1.4)\) Decreasing: \((-1.4,0),(1.4,\infty)\)