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) = □

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

Solution

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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