Combined transformations

Use the sliders to choose values for a and b. For each of the graphs y = af(x) + b, y = f(ax) + b, y = af(x + b) and y = f(ax + b), try to predict the shape of the graph and the coordinates of the local maximum and minimum points, before clicking the check boxes to see each graph. You can zoom in or out if you wish. Click the reset button to go back to the original settings. What happens to each graph if a is negative?