Question

use the indicated graph to identify the intervals over which the function is increasing, constant, or decreasing. (enter your answer using interval notation. if an answer does not exist, enter dne.) increasing (interval with smaller left endpoint) (interval with larger left endpoint) constant decreasing (interval with smaller left endpoint) (interval with larger left endpoint) suggested tutorial: learn it! determine the intervals on which a function is increasing, decreasing, or constant

Explanation:

Step1: Recall the definition of increasing, decreasing and constant 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
• A function \(y = f(x)\) is decreasing on an interval if for any two points \(x_1\) and \(x_2\) in the interval with \(x_1
• A function \(y = f(x)\) is constant on an interval if for any two points \(x_1\) and \(x_2\) in the interval, \(f(x_1)=f(x_2)\).

Step2: Analyze the graph

• For the increasing part:
• Looking at the left - hand side of the graph (where \(x < 0\)), as \(x\) increases (moves from left to right), \(y\) increases. The interval is \((-\infty,0)\). But if we consider the given options, we note that the general form of interval notation for the increasing part (based on the axes range in the graph) is \((-\ 5,0)\) (assuming the \(x\) - axis range in the problem's context).
• For the decreasing part:
• Looking at the right - hand side of the graph (where \(x>0\)), as \(x\) increases (moves from left to right), \(y\) decreases. The interval is \((0,\infty)\). But considering the given options, the interval is \((0,5)\).
• For the constant part:
• There is no part of the graph where the \(y\) - value remains the same for a non - zero length of the \(x\) - interval. So we enter \(DNE\).

Answer:

Increasing: \((-5,0)\); Constant: \(DNE\); Decreasing: \((0,5)\)