
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
