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The Functions area integrates the algebraic line and the Cartesian plane. Expressions on the algebraic line are automatically represented graphically in the Cartesian plane.

This can be used for:
  • constructing meanings for the function, variable and parameter notions. Demo
  • supporting the reading and interpretation of graphs. Demo

The integration between the algebraic line and the Cartesian plane supports two conceptions of function notion:  the dynamic conception developed in the algebraic line and the static conception associated to the graphic in the Cartesian plane. By dragging the mobile point associated to the variable on the algebraic line, both the expression involving that variable in the algebraic line and the point on the curb in the Cartesian plane move accordingly. This integration is important to interpret graphics. For example, it can be used to interpret the intersection between two curbs (observing that the two expressions are coincident in a point on the algebraic line when the variable is on the point of intersection). It is also possible to use the curbs to study the function sign (observing the position of the expression on the line in respect to 0) or to establish an order relationship among functions (observing the position of the corresponding expressions on the line).