Question

question 2 of 22
which of the following functions is graphed below?
(graph of a step - function on a coordinate plane)
a. $y = \lfloor x \
floor - 4$
b. $y = \lfloor x \
floor + 4$
c. $y = \lfloor x \
floor + 6$
d. $y = \lfloor x \
floor - 6$

Explanation:

Step1: Recall the parent function

The parent function of the greatest integer function (floor function) is \( y = \lfloor x
floor \), which has a vertex at \((0, 0)\).

Step2: Analyze the graph's vertical shift

Looking at the graph, we can see that the vertex (the point where the steps change) is at \((0, -6)\). For a vertical shift of the greatest integer function \( y = \lfloor x
floor + k \), if \( k \) is negative, the graph shifts down. Here, the shift is down by 6 units. So the function should be \( y = \lfloor x
floor - 6 \).

Step3: Verify with options

• Option A: \( y = \lfloor x

floor - 4 \) would shift down by 4, not 6.

• Option B: \( y = \lfloor x

floor + 4 \) shifts up by 4.

• Option C: \( y = \lfloor x

floor + 6 \) shifts up by 6.

• Option D: \( y = \lfloor x

floor - 6 \) shifts down by 6, matching the graph.

Answer:

D. \( y = \lfloor x
floor - 6 \)