Question

click on the correct option.

find the function name.

piecewise-linear function

piecewise function

Explanation:

Analyze the graph components

The graph consists of three distinct segments over different intervals of \(x\):

• For \(x < 0\), a linear segment with a negative slope.
• For \(0 \le x < 2\), a linear segment with a positive slope.
• For \(x \ge 2\), a constant horizontal line segment.

Identify the function type

• Since the graph is composed of multiple distinct sub-functions defined on different intervals, it is a piecewise function.
• Since every single sub-function segment is a straight line (linear), the entire function is specifically a piecewise-linear function.
• Looking at the options shown in the interface, "Piecewise-linear function" is displayed directly below the graph, and "Piecewise function" is the active selection in the carousel. "Piecewise-linear function" is the most specific and accurate name for this graph.

Answer:

• (A) Piecewise-linear function (Correct answer)
• (B) Piecewise function