f(x)= ) 2xleqslant 1&if&xleqslant -1 -x+1&if&xgt -1 Choo se the correct graph below. A

To find the correct graph for the given piecewise function, we need to analyze each piece of the function separately.For the first piece, when , the function is defined as . This is a linear function with a slope of 2 and passing through the point (-1, -2).For the second piece, when , the function is defined as . This is also a linear function with a slope of -1 and passing through the point (0, 1).Now let's compare the given options with the piecewise function:Option A: The graph in option A matches the piecewise function. It starts at the point (-1, -2) and follows the line for . Then, it follows the line for , passing through the point (0, 1).Option B: The graph in option B does not match the piecewise function. It does not start at the point (-1, -2) and does not follow the correct lines for each piece of the function.Option C: The graph in option C also does not match the piecewise function. It does not start at the point (-1, -2) and does not follow the correct lines for each piece of the function.Therefore, the correct graph for the given piecewise function is option A.