Question

which of the following graphs shows a piecewise-defined function?
a.
b.
c.
d.

Explanation:

Define piecewise-defined functions

Using the Piecewise Functions knowledge point
A piecewise-defined function is a function represented by multiple distinct sub-functions, each applying to a specific interval of the domain. Visually, this often results in a graph with different shapes, segments, or discontinuities across different intervals.

Analyze the given options

• Graph a: Shows a single continuous absolute value function \(y = |x - h| + k\). It is defined by a single formula.
• Graph b: Shows a parabola on the interval \(x < 2\) (ending with an open circle) and a horizontal ray on the interval \(x \ge 2\) (starting with a closed circle). This is composed of two distinct formulas on different intervals.
• Graph c: Shows a single continuous quadratic function (parabola) defined by a single formula.
• Graph d: Shows a single continuous cubic function defined by a single formula.

Identify the correct graph

Graph b is the only graph composed of distinct sub-functions on different intervals, representing a piecewise-defined function.

Answer:

• a.
• b. (Correct answer)
• c.
• d.