Question

identifying increasing and decreasing intervals which statement is true regarding the intervals where the function is increasing and decreasing? the function is increasing from (-∞, 0). the function is increasing from (0, ∞). the function is decreasing from (-∞, 0). the function is decreasing from (-∞, ∞).

Explanation:

Step1: Recall the definition of increasing and decreasing functions

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 parabola opening downwards), as \(x\) moves from \(-\infty\) to \(0\), the \(y -\) values of the function are getting larger. For example, if we take \(x=-3\) and \(x = - 1\) (\(-3<-1\)), and assume \(y_1=f(-3)\) and \(y_2=f(-1)\), we can see from the graph that \(y_1

When \(x\) moves from \(0\) to \(\infty\), the \(y -\) values of the function are getting smaller. For example, if we take \(x = 1\) and \(x=3\) (\(1 < 3\)), and assume \(y_1=f(1)\) and \(y_2=f(3)\), we can see from the graph that \(y_1>y_2\).

Answer:

The function is increasing from \((-\infty,0)\)