Alberta Math 30-1

GeoGebra Constructions Organized by Strand

Relations and Functions

Functions - Stretches - Practice
  • Given a random function and a random stretch of that function (of the form \( g(x)=af(bx) \) ), determine what \( a,b \) must be
  • Watch the individual stretches to see if your \( a,b \) values are correct
  • Keep practicing with random functions
Functions - Transformations - Animation
  • Enter values for \( a,b,h,k \) and click buttons to watch the individual transformations of \( g(x)=af(b(x−h))+k \) separately
  • For negative \( a \) and \( b \) values, watch the stretch, then see the reflection
  • Also see how a moveable point gets transformed
  • Choose from the following functions:
    \( f(x)=x \) \( f(x) = x^2 \)
    \( f(x) = x^3 \) \( f(x) = \sqrt{x} \)
    \( f(x) = 10^x \) \( f(x) = \log_{10}{x} \)
Functions - Transformations - Animation - Piecewise
  • Enter values for \( a,b,h,k \) and click buttons to watch the individual transformations of \( g(x)=af(b(x−h))+k \) separately
  • For negative \( a \) and \( b \) values, watch the stretch, then see the reflection
  • \( f(x) \) is a piecewise function defined by draggable points
Functions - Transformations - Practice
  • Given a random function and a random transformation of that function (of the form \( g(x)=af(b(x−h))+k) \), determine what \( a,b,h,k \) must be
  • Watch the individual transformations to see if your \( a,b,h,k \) values are correct
  • Keep practicing with random functions
Functions - Transformations - Sliders
  • Use sliders to show how the graph of \( g(x)=af(b(x−h))+k \) is related to the graph of \( f(x) \)
  • Also see how a moveable point gets transformed
  • Choose from the following functions
    \( f(x)=x \) \( f(x) = x^2 \)
    \( f(x) = x^3 \) \( f(x) = \sqrt{x} \)
    \( f(x) = 10^x \) \( f(x) = \log_{10}{x} \)
Functions - Transformations - Sliders - Piecewise
  • Use sliders to show how the graph of \( g(x)=af(b(x−h))+k \) is related to the graph of \( f(x) \)
  • \( f(x) \) is a piecewise function defined by draggable points
Functions - Translations - Practice
  • Given a random function and a random translation of that function (of the form \( g(x)=f(x−h)+k) \) , determine what \( h,k \) must be
  • Watch the individual translations to see if your \( h,k \) values are correct
  • Keep practicing with random functions