Investigation - graphs of the form y = ax^n
Investigation - graphs of
Using the slider, set .
Investigate what happens for different values of . In particular, take note of what is special about the function when (the power) is negative.
Questions:
How can you re-write ^(-b)?
Why does a strange phenomenon occur when n is negative? Does the phenomenon remind you of anything we've already covered (Hint: it should! :D)
Find the similarities between the functions where is the same but they have different signs. (e.g. compare ^(-2) and ).
How does increasing and decreasing affect the functions?