
Absolute Value
 Show how the graphs of \( f(x) \) and \( f(x) \) relate to each other
 Choose from:
 \( f(x)=a(x−b) \)
 \( f(x)=a(x−b)(x−c) \)


Absolute Value  Draggable
 Show how the graphs of \( f(x) \) and \( f(x) \) relate
to each other
 \( f(x) \) is defined by draggable points
 Choose from:
 \( f(x)=ax+b \)
 \( f(x)=ax^2+bx+c \)


Linear  \( y = mx + b \)

Show how the parameters in \( y = mx + b \) are related to the characteristics of the corresponding graph


Quadratic  Expanded Form

Show how the parameters in \( f(x)=ax^2+bx+c \) are related
to the characteristics of the corresponding graph


Quadratic  Factored Form

Show how the parameters in \( f(x)=a(x−b)(x−c) \) are related
to the characteristics of the corresponding graph


Quadratic  Vertex Form

Show how the parameters in \( f(x)=a(x−p)^2+q \) are related
to the characteristics of the corresponding graph


Reciprocal  Polynomials

Show how the graphs of \( f(x) \) and \( \frac{1}{f(x)} \)
relate to each other
 Choose from:
 \( f(x)=a(x−b) \)
 \( f(x)=a(x−b)(x−c) \)


Reciprocal  Polynomials  Draggable

Show how the graphs of \( f(x) \) and \( \frac{1}{f(x)} \)
relate to each other
 f(x) is defined by draggable points
 Choose from:
 \( f(x)=ax+b \)
 \( f(x)=ax^2+bx+c \)


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


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:
\( f(x)=x \) 
\( f(x) = x^2 \) 
\( f(x) = x^3 \) 
\( f(x) = \sqrt{x} \) 
\( f(x) = 10^x \) 
\( f(x) = \log_{10}{x} \) 


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


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


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
\( f(x)=x \) 
\( f(x) = x^2 \) 
\( f(x) = x^3 \) 
\( f(x) = \sqrt{x} \) 
\( f(x) = 10^x \) 
\( f(x) = \log_{10}{x} \) 


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


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
