Question

the graph represents f(x) = ⌊x⌋ + 3. what is f(-2.2)? -2 0 1 2

Explanation:

Step1: Identify the function type

The function \( f(x) = \lfloor x
floor + 3 \) is a floor function (greatest integer function) shifted up by 3. The floor function \( \lfloor x
floor \) gives the greatest integer less than or equal to \( x \).

Step2: Evaluate \( \lfloor -2.2

floor \)
For \( x = -2.2 \), the greatest integer less than or equal to \( -2.2 \) is \( -3 \) (since \( -3 \leq -2.2 < -2 \)).

Step3: Calculate \( f(-2.2) \)

Substitute \( \lfloor -2.2
floor = -3 \) into the function:
\( f(-2.2) = \lfloor -2.2
floor + 3 = -3 + 3 = 0 \).

Answer:

0