Transforming functions

Transforming functions Trasformazione di funzioni Transformation des fonctions تحويل الدالات कार्य बदलना 函数图像变换 Verschuif functies Transformar funciones Transforamando frações


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.