graph the piece - wise - defined function. f(x)={-3 - x if x≤1, -3 + 2x if x>1}. choose the correct graph…

Explanation:

Step1: Analyze (y = - 3 - x) for (x\leq1)

When (x = 1), (y=-3 - 1=-4). The slope of (y=-3 - x) is (- 1). The line is solid at (x = 1) (since (x\leq1)) and has a (y) - intercept of (-3).

Step2: Analyze (y=-3 + 2x) for (x>1)

When (x = 1), (y=-3+2\times1=-1). The slope of (y=-3 + 2x) is (2). The line is dashed at (x = 1) (since (x>1)).

Step3: Check the graphs

Examine each option to see which one has a solid - line part for (y=-3 - x) when (x\leq1) and a dashed - line part for (y=-3 + 2x) when (x>1) with the correct slopes and intercepts.

Answer:

(Without seeing the full - clarity of the options, we can't give a specific letter - choice answer. But the above steps can be used to identify the correct graph among A, B, C, D).