Question

use the graph to answer the question. find the interval(s) over which the function is increasing. (1 point) (0,1)∪(1,∞) (-∞,-1)∪(-1,0) (-∞,-1) (1,∞)

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 graph

Looking at the graph of the function (a rational - like function with two branches), for the positive - \(x\) side (right of the \(y\) - axis), when \(x>0\), as \(x\) increases, the \(y\) - values of the function decrease. For the negative - \(x\) side (left of the \(y\) - axis), when \(x\in(-\infty, - 1)\), as \(x\) increases (i.e., moves from left to right on the interval \((-\infty,-1)\)), the \(y\) - values of the function increase.

Answer:

\((-\infty,-1)\)