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Mathematics LibreTexts

11.2: Presenting Results with Visualization, an overview

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11.2.1 Plotting Functions and other Curves

Mathematically speaking, we often this about functions. However, functions can take on many forms including:

  • functions of one variable–plots of this are often function plots with the independent variable on the horizontal axis and function values on the vertical. We saw such function graphs above.

  • parametric functions (vector functions in 2D). These are functions in which the x and y variables depend on a parameter (often t or θ). We will see how to plot this in section XXX

  • implicit curves .An implicit curve is the set of points (x,y) in which f(x,y)=0.The classic example is the circle
    x2+y2=1


    which can be written in the form f (x, y) = 0 by subtracting 1 from both sides.

  • functions of two variables. These often have the form:
    z=f(x,y)


    and that the two independent variables are x and y and the third variable is the height of the function. There are at least three standard ways of representing such a function:

    • surface plots as in section 11.3.3 which is a 3D rendering of the surface

    • contour plots (section ??), which generates a curve in the plane for a given

      number of heights.

    • heatmaps (section??) which gives a color representing the height of the function.

    • Vector Functions in 3D are often represented as parametric functions of the form:
      x(t),y(t),z(t)


      where each function gives the x,y or z coordinate at a time t. Examples of this are in section XXX


11.2: Presenting Results with Visualization, an overview is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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