Transformations of functions: Horizontal translations

Everything You Need in One Place

Homework 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 Ease

Our 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 Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

Get the most by viewing this topic in your current grade. Pick your course now.

?
Examples
Start Watching
Lessons
    1. Sketch the following functions on the same set of coordinate axes:
      y=(x)2y = {\left( x \right)^2}      VS.      y=(x−6)2y = {\left( {x - 6} \right)^2}      VS.      y=(x+5)2y = {\left( {x + 5} \right)^2}
    2. Compared to the graph of y=x2y = {x^2}:
      • the graph of y=(x−6)2y = {\left( {x - 6} \right)^2} is translated "horizontally" ________ units to the ______________.
      • the graph of y=(x+5)2y = {\left( {x + 5} \right)^2} is translated "horizontally" ________ units to the ______________.
  2. Horizontal Translations
    Given the graph of y=f(x)y = f\left( x \right) as shown, sketch:
    1. y=f(x−8)y = f\left( {x-8} \right)
    2. y=f(x+3)y = f\left( {x+3} \right)
    3. In conclusion:
      • (x)→(x−8)\left( x \right) \to \left( {x-8} \right): shift __________ to the __________. All x coordinates ⇒\Rightarrow ____________________
      • (x)→(x+3)\left( x \right) \to \left( {x+3} \right): shift __________ to the __________. All x coordinates ⇒\Rightarrow ____________________
      Vertical translations
Free to Join!
StudyPug is a learning help platform covering math and science from grade 4 all the way to second year university. Our video tutorials, unlimited practice problems, and step-by-step explanations provide you or your child with all the help you need to master concepts. On top of that, it's fun - with achievements, customizable avatars, and awards to keep you motivated.

  • Easily See Your Progress

    We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.

  • Make Use of Our Learning Aids

    Last Viewed
    Practice Accuracy
    Suggested Tasks

    Get quick access to the topic you're currently learning.

    See how well your practice sessions are going over time.

    Stay on track with our daily recommendations.

  • Earn Achievements as You Learn

    Make the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.

  • Create and Customize Your Avatar

    Play with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.
Topic Notes
?
Horizontal translations refer to movements of a graph of a function horizontally along the x-axis by changing the x values. So, if y = f(x), then y = (x –h) results in a horizontal shift. If h > 0, then the graph shifts h units to the right; while If h < 0, then the graph shifts h units to the left.
Compared to y=f(x)y=f(x):
y=f(x−8)y=f(x-8): shift 8 units to the right
y=f(x+3)y=f(x+3): shift 3 units to the left
Basic Concepts
?
Related Concepts
?