Transforming functions

Transforming functions Trasformazione di funzioni


Transforming functions

Enter your function here.


How shall your function be transformed?

By in x-direction

By in y-direction

By to the

By to the

How to transform the graph of a function?

This depends on the direction you want to transoform. In general, transformations in y-direction are easier than transformations in x-direction, see below.

How to move a function in y-direction?

Just add the transformation you want to to. This is it. For example, lets f_f(x)=x^3-2x-2 move this Graph by 5 units to the top.


Your exercise:
The function f(x)=1*x^3+-2*x+-2 shall be moved by

5 to up

Graph before the transformation: :
Dein Browser unterstützt den HTML-Canvas-Tag nicht. Hol dir einen neuen. :P
    Function after the transformation: f(x)=1*x^3+-2*x+3
    Dein Browser unterstützt den HTML-Canvas-Tag nicht. Hol dir einen neuen. :P
      This is what Mathepower calculated:

      Move the graph of f(x)=1*x^3+-2*x+-2 by 5 in direction up
      Add 5 to the function.
      Moved function: f(x)=1*x^3+-2*x+-2+5


      Simplify the new function: :
      | add -2 to 5
      1*f(x)=1*x^3+-2*x+-2+5

      How to move a function in x-direction?

      If you want to move in x-direction, it is more difficult for two reasons:
      • You have to replace every x by x-2
      • and mind the sign: If you want to go in x-direction, replace x by x-2. But if you want to go in the opposite direction, you replace x by x+2?!?...
      Here is another example involving the latter function.


      Your exercise:
      The function f(x)=1*x^3+-2*x+-2 shall be moved by

      2 to the right

      Graph before the transformation: :
      Dein Browser unterstützt den HTML-Canvas-Tag nicht. Hol dir einen neuen. :P
        Function after the transformation: f(x)=1*x^3+-6*x^2+10*x+-6
        Dein Browser unterstützt den HTML-Canvas-Tag nicht. Hol dir einen neuen. :P
          This is what Mathepower calculated:

          Move the graph of f(x)=1*x^3+-2*x+-2 by 2 in direction right :
          Replace every x by (x+-2)
          Moved function: f(x)=1*(x+-2)^3+-2*(x+-2)+-2


          Simplify the new function: :
          | Apply the higher binomial formula (a+b)^3=a^3+3*a^2*b^1+3*a^1*b^2+b^3 with a=1*x and b=-2
          1*f(x)=1*(x^3+-6*x^2+12*x+-2^3)+-2*(1*x+-2)+-2| Calculate -2 to the power of 3 .
          1*f(x)=1*(1*x^3+-6*x^2+12*x+-8)+-2*(1*x+-2)+-2| Expand -2 and (1*x+-2) .
          1*f(x)=(1*x^3+-6*x^2+12*x+-8)+(-2*x+4)+-2
          1*f(x)=(1*x^3+-6*x^2+12*x+-8)+-2*x+4+-2| add 4 to -2
          1*f(x)=(1*x^3+-6*x^2+12*x+-8)+-2*x+2| add -8 to 2
          1*f(x)=1*x^3+-6*x^2+12*x+-2*x+-8+2| add 12*x to -2*x
          1*f(x)=1*x^3+-6*x^2+10+-2*x+-6

          How to stretch a function in y-direction?

          This is easy, again: Just multiply your whole function by the stretching factor. For example, lets stretch f_f(x)=x^3-x by Factor 2 in y-direction.


          Your exercise:
          The function f(x)=x^3+-1*x shall be moved by

          2 in y-direction stretched

          Graph before the transformation: :
          Dein Browser unterstützt den HTML-Canvas-Tag nicht. Hol dir einen neuen. :P
            Function after the transformation: f(x)=(2*x^3+-2*x)
            Dein Browser unterstützt den HTML-Canvas-Tag nicht. Hol dir einen neuen. :P
              This is what Mathepower calculated:

              Transform the function f(x)=x^3+-1*x by 2 in y-direction stretch :
              Multiply the function by 2
              Stretched function f(x)=2*(x^3+-1*x)


              Simplify the new function: :
              | Expand 2 and (1*x^3+-1*x) .
              1*f(x)=2*x^3+-2*x

              How to stretch a function in x-direction?

              Again, like moving, stretchig is more difficult: We have to replace every x by x/2 (Mind that it is again not the way you may think: Stretching does not mean multiplying by 2, but dividing by 2!)


              Your exercise:
              The function f(x)=x^3+-1*x shall be moved by

              2 in x-direction stretched

              Graph before the transformation: :
              Dein Browser unterstützt den HTML-Canvas-Tag nicht. Hol dir einen neuen. :P
                Function after the transformation: f(x)=1*1/2^3*x^3+-1/2*x
                Dein Browser unterstützt den HTML-Canvas-Tag nicht. Hol dir einen neuen. :P
                  This is what Mathepower calculated:

                  Transform the function f(x)=x^3+-1*x by 2 in x-direction stretch :
                  Replace every x by (x/2)
                  Stretched function f(x)=(x/2)^3+-1*(x/2)


                  Simplify the new function: :
                  | Extract (x) from the fraction
                  1*f(x)=1*1/2*x^3+-1*(x/2)| Solve with the power laws : 1/2*x^3 equals 1/2^3*x^3
                  1*f(x)=1*1/2^3*x^3+-1*(x/2)| Extract (x) from the fraction
                  1*f(x)=1*1/2^3*x^3+-1*1/2*x

                  And if I want to move another function?

                  This is Mathepower. Just enter it above.