Introduction to Twelve Basic Functions

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Key Questions

    1. Identity: #f(x) = x#
    2. Square: #f(x) = x^2#
    3. Cube: #f(x) = x^3#
    4. Reciprocal: #f(x)=1/x = x^(-1)#
    5. Square Root: #f(x) = sqrt(x) = x^(1/2)#
    6. Exponential: #f(x) = e^x#
    7. Logarithmic: #f(x) = ln(x)#
    8. Logistic: #f(x) = 1/(1+e^(-x))#
    9. Sine: #f(x) = sin(x)#
    10. Cosine: #f(x)=cos(x)#
    11. Absolute Value: #f(x) = abs(x)#
    12. Integer Step: #f(x)= "int"(x)#
  • The Sine function: #f(x) = sin(x)#
    The Cosine function: #f(x) =cos(x)#
    and
    The Logistic function: #f(x) = 1/(1-e^(-x))#
    are the only function of the "Basic Twelve Functions" which are bounded above.

  • Of the 12 Basic F|unctions only
    The identity function: #f(x)=x#
    and
    The reciprocal function: #f(x)=1/x#
    are their own inverses.

Questions