Addition and Subtraction of Functions

Addition of functions is a pointwise operation:

$(f + g)(x) = f(x) + g(x).$

Subtraction is defined similarly as

$(f - g)(x) = f(x) - g(x).$

In the applet below, the graphs of both $f\,$ and $g\,$ could be dragged up and down at any point. This will automatically change the result of the operation. The graph of $f\,$ is depicted in black and that of $g\,$ in green. For the sum $(f + g),\,$ I use blue, and for the difference $(f - g)\,$ red color. Thus of the three graphs only two -- the black and the green -- are draggable.

If you are reading this, your browser is not set to run Java applets. Try IE11 or Safari and declare the site as trusted in the Java setup.

Operations on functions

What if applet does not run?

Related material

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  • Cartesian Coordinate System
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  • Graph of a Polynomial of arbitrary degree
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  • Inflection Points of Fourth Degree Polynomials
  • Lagrange Interpolation (an Interactive Gizmo)
  • Equations of a Straight Line
  • Taylor Series Approximation to Cosine
  • Taylor Series Approximation to Cosine
  • Linear Function with Coefficients in Arithmetic Progression
  • Sine And Cosine Are Continuous Functions
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