f(x)=\\begin{cases}1 & \\text{if } - 1 < x \\leq 0 \\\\2 & \\text{if }0 < x \\leq 1 \\\\3 & \\text{if }1 < x…

f(x)=\\begin{cases}1 & \\text{if } - 1 < x \\leq 0 \\\\2 & \\text{if }0 < x \\leq 1 \\\\3 & \\text{if }1 < x \\leq 2\\end{cases}\nthen determine which answer choice matches the graph you drew.

Answer

Explanation:

Step1: Analyze first - interval

For (-1 < x\leq0), (y = 1). This is a horizontal line segment with an open - circle at (x=-1) (since (x > - 1)) and a closed - circle at (x = 0) (since (x\leq0)).

Step2: Analyze second - interval

For (0 < x\leq1), (y = 2). This is a horizontal line segment with an open - circle at (x = 0) (since (x>0)) and a closed - circle at (x = 1) (since (x\leq1)).

Step3: Analyze third - interval

For (1 < x\leq2), (y = 3). This is a horizontal line segment with an open - circle at (x = 1) (since (x>1)) and a closed - circle at (x = 2) (since (x\leq2)).

Step4: Match the graph

The graph that has horizontal line segments at (y = 1) for (-1 < x\leq0), (y = 2) for (0 < x\leq1) and (y = 3) for (1 < x\leq2) with the correct open and closed circles is graph B.