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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
      \[ x^2+y^2=1\]
      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:
        \[ \langle x(t),y(t),z(t) \rangle\]
        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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