Questions: The greatest integer function is defined by int (x) = the greatest integer that is less than or equal to x. int(7.7) = 7 int(-4.9) = □

The greatest integer function is defined by int (x) = the greatest integer that is less than or equal to x. int(7.7) = 7 int(-4.9) = □
Transcript text: The greatest integer function is defined by int $(x)=$ the greatest integer that is less than or equal to $x$. $\operatorname{int}(7.7)=7$ $\operatorname{int}(-4.9)=$ $\square$
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Solution

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Solution Steps

To find the greatest integer function value for \(\operatorname{int}(-4.9)\), we need to determine the largest integer that is less than or equal to \(-4.9\). This involves identifying the integer part of the number when rounded down.

Step 1: Understanding the Greatest Integer Function

The greatest integer function, denoted as \(\operatorname{int}(x)\), returns the largest integer less than or equal to \(x\). For a given real number \(x\), this function effectively "rounds down" to the nearest integer.

Step 2: Applying the Function to \(-4.9\)

Given \(x = -4.9\), we need to find the greatest integer less than or equal to \(-4.9\). Since \(-5\) is the largest integer that is less than \(-4.9\), we have:

\[ \operatorname{int}(-4.9) = -5 \]

Final Answer

\[ \boxed{-5} \]

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