Visualizing Square Root and Absolute Value
Visualizing Square Root and Absolute Value
Taking the absolute value of a number leaves the number unchanged if the number is nonnegative and changes the sign of the number otherwise. Thus, when you take the absolute value of a function, the effect on the graph is to leave portions above the axis unchanged and to reflect portions below the axis through the axis.
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You can only take (real) square roots of nonnegative numbers, so when you take the square root of a function, the portion of the graph below the axis disappears, while the portion above the axis is distorted by the taking of square roots.
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In this Demonstration, you can take the square root or absolute value of a function and see the effect. The original function is shown as a purple, dashed curve. If both boxes are checked, the graph shown will be that of , because is the same as for realvalued .
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