Affine approximations

The graph on the right is a plot of the absolute value of the error in approximating the square root function by an affine function passing through (1,1) with the specified slope m. That is, the graph on the right is the graph of the absolute value of

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The Zoom in button changes the scale of the graph on the right by a factor of 0.5 in the horizontal direction and 0.25 in the vertical direction; the Zoom out button changes the scale of the graph on the right by a factor of 2 in the horizontal direction and 4 in the vertical direction.