Q8. - Algebra 1

Question

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

 

The range of the greatest integer function is the set of all real numbers

Step-by-Step Solution

Answer

The given statement is False. The corrected statement is:

“The domain of the greatest integer function is the set of all real numbers.”

Step 1. State the concept.

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.

Step 2. Explanation of the statement.

Greatest Integer Function:

Parent Function: $f\left(x\right)=〚x〛$

Type of Graph: disjointed line segments

Domain: All real numbers

Range: All integers

Graph:

 

$\boxed{f\left(x\right)=〚x〛}$

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

Clearly, from the explanation, it can be observed that the domain of the Greatest Integer function is all real numbers whereas the range is all integers, therefore, the given statement is False. The corrected statement is:

“The domain of the greatest integer function is the set of all real numbers.”