Question

question 26 points 1

the given graph is an example of _________ function.

• non-linear
• piecewise-defined

Explanation:

Analyze the graph's structure

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

• For \(x \in [-4, -1]\), it is a curved segment (part of a parabola).
• For \(x \in [-1, 2]\), it is a decreasing linear segment.
• For \(x \in [2, 5]\), it is a constant horizontal line.

Identify the function type

A function that is defined by multiple sub-functions, each applying to a certain interval of the domain, is called a piecewise-defined function.

Answer:

The given graph is an example of <blank>piecewise-defined</blank> function.

• non-linear
• piecewise-defined (Correct answer)