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Exploring Cubic Functions
Age 14 to 18
Challenge Level 
When working with functions and their graphs, here are a few key points to look out for:
Where does the graph cross the $x$ axis? (We call these the roots of the function)
Where does it cross the $y$ axis?
Does the graph have any reflectional or rotational symmetry?
Does the graph have any turning points?
Sketching Graphs - Transformations includes a video about the relationship between functions whose graphs are translations of each other.
When using the GeoGebra applets it might be a good idea to start the slider(s) at 0.
When you have two sliders, you could start by exploring the effect of moving each separately before exploring the effect of moving both together.
Where does the graph cross the $x$ axis? (We call these the roots of the function)
Where does it cross the $y$ axis?
Does the graph have any reflectional or rotational symmetry?
Does the graph have any turning points?
Sketching Graphs - Transformations includes a video about the relationship between functions whose graphs are translations of each other.
When using the GeoGebra applets it might be a good idea to start the slider(s) at 0.
When you have two sliders, you could start by exploring the effect of moving each separately before exploring the effect of moving both together.
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