Question

evaluate the floor function f(x) = \lfloor x \
floor for the given input values.
f(2) =
f(6.8) =
f(-3.3) =

Explanation:

Step1: Recall the floor function definition

The floor function \( \lfloor x
floor \) gives the greatest integer less than or equal to \( x \).

Step2: Evaluate \( f(2) \)

For \( x = 2 \), the greatest integer less than or equal to 2 is 2. So \( f(2)=\lfloor 2
floor = 2 \).

Step3: Evaluate \( f(6.8) \)

For \( x = 6.8 \), the greatest integer less than or equal to 6.8 is 6 (since 6 ≤ 6.8 < 7). So \( f(6.8)=\lfloor 6.8
floor = 6 \).

Step4: Evaluate \( f(-3.3) \)

For \( x = -3.3 \), we look for the greatest integer less than or equal to -3.3. The integers less than -3.3 are -4, -5, etc., and the greatest one among them is -4 (since -4 ≤ -3.3 < -3). So \( f(-3.3)=\lfloor -3.3
floor = -4 \).

Answer:

\( f(2) = \boldsymbol{2} \), \( f(6.8) = \boldsymbol{6} \), \( f(-3.3) = \boldsymbol{-4} \)