Question

using the graph below, what are the values of the domain that provide a constant interval?

source:
image created for vva via desmos; 2025

\\(2 \le x \le 4\\)
\\(x \le 1\\)
\\(x < 1\\)
\\(x > 2\\)

Explanation:

Identify the constant interval

Using the Reading Function Graphs knowledge point, a constant interval on a graph is represented by a horizontal line segment where the \(y\)-value does not change as \(x\) increases. Looking at the graph, there is a horizontal line at \(y = 1\) extending to the left.

Determine the domain of the constant interval

Using the Piecewise Functions knowledge point, we find the \(x\)-values corresponding to this horizontal section. The horizontal line starts from the far left (representing \(-\infty\)) and ends at the solid point at \(x = 1\). Because the point at \(x = 1\) is solid, the value \(x = 1\) is included in this interval. Therefore, the domain for this constant interval is \(x \le 1\).

Answer:

• (A) \(2 \le x \le 4\)
• (B) \(x \le 1\) (Correct answer)
• (C) \(x < 1\)
• (D) \(x > 2\)