Transformations of functions: Horizontal translations
Everything You Need in One PlaceHomework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.  Learn and Practice With EaseOur proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.  Instant and Unlimited HelpOur personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now! 
Make math click 🤔 and get better grades! 💯Join for Free
Get the most by viewing this topic in your current grade. Pick your course now.
Examples
Lessons

 Sketch the following functions on the same set of coordinate axes:
$y = {\left( x \right)^2}$ VS. $y = {\left( {x  6} \right)^2}$ VS. $y = {\left( {x + 5} \right)^2}$  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 ______________.
 Sketch the following functions on the same set of coordinate axes:
 Horizontal Translations
Given the graph of $y = f\left( x \right)$ as shown, sketch: $y = f\left( {x8} \right)$
 $y = f\left( {x+3} \right)$
 In conclusion:
• $\left( x \right) \to \left( {x8} \right)$: shift __________ to the __________. All x coordinates $\Rightarrow$ ____________________
• $\left( x \right) \to \left( {x+3} \right)$: shift __________ to the __________. All x coordinates $\Rightarrow$ ____________________