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.<br /><br />For the first piece, when $x \leqslant -1$, the function is defined as $f(x) = 2x$. This is a linear function with a slope of 2 and passing through the point (-1, -2).<br /><br />For the second piece, when $x > -1$, the function is defined as $f(x) = -x + 1$. This is also a linear function with a slope of -1 and passing through the point (0, 1).<br /><br />Now let's compare the given options with the piecewise function:<br /><br />Option A: The graph in option A matches the piecewise function. It starts at the point (-1, -2) and follows the line $f(x) = 2x$ for $x \leqslant -1$. Then, it follows the line $f(x) = -x + 1$ for $x > -1$, passing through the point (0, 1).<br /><br />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.<br /><br />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.<br /><br />Therefore, the correct graph for the given piecewise function is option A.