# 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