The Wonderful World of Functions

f(x)=x^2

          Domain: All Reals!
         Range: y is greater than or equal to 0
         Zeros: x=0
         Symmetry with the y-axis
         Even function
         This function is not periodic
         ...or a one-to-one

f(x)=x^3
         Domain: All Reals!
         Range: All Reals Again!
         Zeros: x=0
         Symmetry with the origin
         This is an odd function
         Not periodic
         But it is one-to-one!

f(x)=abs(x)
         Domain: All Reals!
         Range: y greater than/equal to 0
         Zeros: x=0
         Symmetry with the y-axis
         This is an even function
         Not periodic
         ...or one-to-one

f(x)=sinx
        Domain: All Reals!
        Range: abs(x) less than/equal to 1
        x=kπ
       Symmetry with the origin
       This is an odd function
       It is a periodic trig function!
       But it isn't one-to-one

f(x)=cosx
         Domain: All Reals!
         Range: abs(y) less than/equal to 1
         Zeros: x=(2k+1)π/2
        Symmetry with the y-axis
        This is an even function
        It is periodic
        But it is not one-to-one

f(x)=tanx
         Domain: x not equal to (2k+1)π/2
        Range: All Reals!
        Zeros: x=kπ
        Symmetry with the origin
        This is an odd function
        It is periodic!
        But it is not one-to-one!

f(x)=secx
         Domain: x does not equal (2k+1)π/2
        Range: abs(y) greater/equal to 1
        No Zeros
        Symmetry with the y-axis
        This is an even function
        It is periodic!
        But it is not one-to-one

f(x)=2^x
         Domain: All Reals!
         Range: y is greater than 0
         No zeros
         No symmetry
         Neither even or odd
         This is not periodic
         It is one-to-one

f(x)=log(sub2)x
         Domain: x is greater than 0
         Range: All Reals!
         Zeros: x=1
         No symmetry
         Neither odd or even
         It is not periodic
         But it is one-to-one!

f(x)=1/x
         Domain: x cannot equal 0
         Range: y cannot equal 0
         No zeros
         Symmetry with the origin
         This is an odd function
         It is not periodic
         It is one-to-one

f(x)=sqrt(x)
         Domain: x greater than/equal to 0
         Range: y greater than/equal to 0
         Zeros: x=0
         No symmetry
         Neither or odd or even
         This is not periodic
         But it is one-to-one

f(x)=sqrt(a^2-x^2)
       Domain: abs(x) less than/equal to a
       Range: 0≤y≤a
       Zeros: x=+a,-a
       Symmetry with the y-axis
       This is an even function
       It is not periodic
       ...or one-to-one

                              THE END

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