which statement describes the graph of $f(x)=\\lfloor x\\rfloor - 2$ on $0,3)$?\nthe steps are at $y = - 2$…

which statement describes the graph of $f(x)=\\lfloor x\\rfloor - 2$ on $0,3)$?\nthe steps are at $y = - 2$ for $0\\leq x<1$, at $y=-1$ for $1\\leq x<2$, and at $y = 0$ for $2\\leq x<3$.\nthe steps are at $y = 0$ for $0\\leq x<1$, at $y = 1$ for $1\\leq x<2$, and at $y = 2$ for $2\\leq x<3$.\nthe steps are at $y = 1$ for $0\\leq x<1$, at $y = 2$ for $1\\leq x<2$, and at $y = 3$ for $2\\leq x<3$.\nthe steps are at $y=-3$ for $0\\leq x<1$, at $y=-2$ for $1\\leq x<2$, and at $y=-1$ for $2\\leq x<3$.

which statement describes the graph of $f(x)=\\lfloor x\\rfloor - 2$ on $0,3)$?\nthe steps are at $y = - 2$ for $0\\leq x<1$, at $y=-1$ for $1\\leq x<2$, and at $y = 0$ for $2\\leq x<3$.\nthe steps are at $y = 0$ for $0\\leq x<1$, at $y = 1$ for $1\\leq x<2$, and at $y = 2$ for $2\\leq x<3$.\nthe steps are at $y = 1$ for $0\\leq x<1$, at $y = 2$ for $1\\leq x<2$, and at $y = 3$ for $2\\leq x<3$.\nthe steps are at $y=-3$ for $0\\leq x<1$, at $y=-2$ for $1\\leq x<2$, and at $y=-1$ for $2\\leq x<3$.

Answer

Explanation:

Step1: Recall the definition of the floor - function

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

Step2: Analyze the function for $0\leq x < 1$

When $0\leq x < 1$, $\lfloor x\rfloor=0$. Then $f(x)=\lfloor x\rfloor - 2=0 - 2=-2$.

Step3: Analyze the function for $1\leq x < 2$

When $1\leq x < 2$, $\lfloor x\rfloor = 1$. Then $f(x)=\lfloor x\rfloor - 2=1 - 2=-1$.

Step4: Analyze the function for $2\leq x < 3$

When $2\leq x < 3$, $\lfloor x\rfloor=2$. Then $f(x)=\lfloor x\rfloor - 2=2 - 2=0$.

Answer:

The steps are at $y = - 2$ for $0\leq x < 1$, at $y=-1$ for $1\leq x < 2$, and at $y = 0$ for $2\leq x < 3$.