Transforming Graphs

Transforming Graphs

1. Translation

   • y-direction
     • f(x) + k
       • Graph translates up the y scale by k units
     • f(x) - k
       • Graph translates down the y scale by k units
   • x-direction
     • f(x+k)
       • Graph translates in the negative x-direction by k units
     • f(x-k)
       • Graph translates in the positive x-direction by k units

2. Reflection

   • In the x-axis
     • -f(x)
     • y values become negative, so reflected in the x-axis
   • In the y-axis
     • f(-x)
     • x values become negative, so reflected in the y-axis

3. Stretch

   • y-direction
     • y=kf(x)
     • Stretch in the y-direction, scale factor k
   • x-direction
     • y=f(kx)
     • Stretch in the x-direction, scale factor 1/k

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