Evaluate f(-3), f(0), and f(2) for the piecewise defined function. Then sketch the graph of the function. f (x) = x + 1 if x less than or equal to -1 x^2 if x greater than -1

To evaluate f(-3), we use the first part of the piecewise function, and substitute -3 for x: f(-3) = -3 + 1 = -2. To evaluate f(0), we use the second part of the piecewise function, and substitute 0 for x: f(0) = 0^2 = 0. To evaluate f(2), we use the second part of the piecewise function, and substitute 2 for x: f(2) = 2^2 = 4. To sketch the graph of the function, we draw a straight line with slope 1 passing through (-1,0) and extending to the left, and a parabolic curve opening upwards with vertex at (-1,1) to the right of it. The graph will look like two separate curves joined at the point (-1,1). The y-axis intercept is (0,1), and the x-axis intercepts are (-2,0) and (1,0). The graph will never dip below the x-axis.