Visualizing square root and absolute value

Taking the absolute value of a number leaves the number unchanged if the number is non-negative 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 x axis unchanged and to reflect portions below the x axis through the x axis. You can only take (real) square roots of non-negative numbers, so when you take the square root of a function, the portion of the graph below the x axis disappears, while the portion above the x axis is distorted by the taking of square roots.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 sqrt(|x|), because |sqrt(x)| is the same as sqrt(x) for real-valuedComponente Curricular::Ensino Médio::MatemáticaComponente Curricular::Educação Superior::Ciências Exatas e da Terra::Matemátic