Question

use the graph to answer the question.
find the interval(s) over which the function is constant.
(1 point)
$(-\infty,-4)$
$(-\infty,3)$
$(2,\infty)$
$(-\infty,-4)\cup(2,\infty)$

Explanation:

Step1: Recall the definition of a constant function

A function \(y = f(x)\) is constant on an interval if for any \(x_1,x_2\) in that interval, \(f(x_1)=f(x_2)\). Visually, the graph of a constant function is a horizontal line.

Step2: Analyze the given graph

Looking at the graph, we see that the part of the graph that is a horizontal line (where the function is constant) occurs for \(x\) values from \(-\infty\) to \(- 4\). There is no other interval where the function is a horizontal line. The intervals \((-\infty,3)\), \((2,\infty)\) and \((-\infty,-4)\cup(2,\infty)\) do not represent the horizontal - line part of the graph.

Answer:

\((-\infty,-4)\)