Practice Test

Question 6 • Algebra 2 with Probability

Which of the following describes the graph of y is equal to lfloor x minus 2 rfloor ?

Answer

The graph has open circles on the left of each step and closed circles on the right and includes the step y is equal to negative 3 for negative 2 is less than or equal to x comma x is less than negative 1 .

The graph has closed circles on the left of each step and open circles on the right and includes the step y is equal to negative 4 for negative 2 is less than or equal to x comma x is less than negative 1 .

The graph has open circles on the left of each step and closed circles on the right and includes the step y is equal to negative 4 for negative 2 is less than or equal to x comma x is less than negative 1 .

The graph has closed circles on the left of each step and open circles on the right and includes the step y is equal to negative 3 for negative 2 is less than x comma x is less than or equal to negative 1 .

Explanation

The floor function gives the greatest integer less than or equal to its input, so each step is closed on the left and open on the right. When −2 ≤ x < −1, subtracting 2 gives −4 ≤ x − 2 < −3, so ⌊x − 2⌋ = −4 throughout that interval. This matches choice A: closed left endpoints, open right endpoints, and a step at y = −4.

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