Transformations of functions: Horizontal translations

Lessons

1. 1. Sketch the following functions on the same set of coordinate axes:
      $y = {\left( x \right)^2}$      VS.      $y = {\left( {x - 6} \right)^2}$      VS.      $y = {\left( {x + 5} \right)^2}$
   2. Compared to the graph of $y = {x^2}$:
      • the graph of $y = {\left( {x - 6} \right)^2}$ is translated "horizontally" ________ units to the ______________.
      • the graph of $y = {\left( {x + 5} \right)^2}$ is translated "horizontally" ________ units to the ______________.
2. Horizontal Translations
   Given the graph of $y = f\left( x \right)$ as shown, sketch:
   1. $y = f\left( {x-8} \right)$
   2. $y = f\left( {x+3} \right)$
   3. In conclusion:
      • $\left( x \right) \to \left( {x-8} \right)$: shift __________ to the __________. All x coordinates $\Rightarrow$ ____________________
      • $\left( x \right) \to \left( {x+3} \right)$: shift __________ to the __________. All x coordinates $\Rightarrow$ ____________________