Step Functions — Quiz

Question 13 • Algebra 2 with Probability

Which statement describes the graph of f of x is equal to lfloor x rfloor minus 2 on left bracket 0 comma 3 right parenthesis ?

Answer

The steps are at y is equal to 1 for 0 is less than or equal to x comma x is less than 1 , at y is equal to 2 for 1 is less than or equal to x comma x is less than 2 , and at y is equal to 3 for 2 is less than or equal to x comma x is less than 3 .

The steps are at y is equal to negative 3 for 0 is less than or equal to x comma x is less than 1 , at y is equal to negative 2 for 1 is less than or equal to x comma x is less than 2 , and at y is equal to negative 1 for 2 is less than or equal to x comma x is less than 3 .

The steps are at y is equal to negative 2 for 0 is less than or equal to x comma x is less than 1 , at y is equal to negative 1 for 1 is less than or equal to x comma x is less than 2 , and at y is equal to 0 for 2 is less than or equal to x comma x is less than 3 .

The steps are at y is equal to 0 for 0 is less than or equal to x comma x is less than 1 , at y is equal to 1 for 1 is less than or equal to x comma x is less than 2 , and at y is equal to 2 for 2 is less than or equal to x comma x is less than 3 .

Explanation

The floor function ⌊x⌋ equals 0 on [0, 1), 1 on [1, 2), and 2 on [2, 3). Subtracting 2 gives the step heights −2, −1, and 0, respectively, which matches the statement in choice A.

AI-written and checked against the verified answer.

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