Transformations of functions: Horizontal translations

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Now Playing:Transformations of functions horizontal translations– Example 1

Horizontal Translations: move the graph of a function left or right.
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 ______________.
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 $\Rightarrow$ ____________________

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