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.

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Operations on functions

What if applet does not run?

Related material

  • What Is Line?
  • Functions, what are they?
  • Cartesian Coordinate System
  • Function, Derivative and Integral
  • Graph of a Polynomial of arbitrary degree
  • Graph of a Polynomial Defined by Its Roots
  • 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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