Question

State whether each sentence is true or false. If false, replace the underlined word, phrase, expression, or number to make a true sentence.

A piecewise-linear function is also called a step function.

Short answer

The given statement is True.

Step-by-step solution

Step 1. State the concept.

Step Function: The graph of a step function is a series of line segments.

For example – the Greatest Integer function

Greatest Integer Function, written as $f\left(x\right)=〚x〛$, where $f\left(x\right)$is the greatest integer not greater than $x$. For example, $〚6.8〛=6$ because 6 is the greatest integer that is not greater than 6.8.

$\boxed{f\left(x\right)=〚x〛}$

Step 2. Explanation of the statement. 

From the graph of a step function, it can be observed that each part of a step function is linear, therefore, this type of function is called a piecewise-linear function.

Step 3. Write whether the statement is true or false.

The given statement “A piecewise-linear function is also called a step function.” Is true.