This tool allows you to input a function, fix a base point on its graph, and then see how moving a variable point on the graph changes "h" and the slope of the secant line connecting the two points.
Input your function in the indicated input box. Use the slider to change the base point x-coordinate, i.e. x_0. The point B is (x_0, f(x_0)); the red point A is at coordinates (x_0 + h, f(x_0 + h)). The value of "h" is displayed in blue, and the slope m of the segment connecting A and B is displayed in brown. The directed length "h" is illustrated by the blue segment on the x-axis. When A is to the left of B this h is negative; and it is positive when A is to the right of B.