Amanda wants to showcase her favorite function:
What is Eric's equation for his function
What happens if the two machines are pushed together? What is
? Explain why this happens.
Try several values for
in . is a very convenient value to use. So are and .
What happens in each case?
and are graphed on the same set of axes, what would be true about the two graphs?
What characteristic has been common to all function-inverse pairs that you have graphed before?
Draw the two graphs on the same set of axes. Be sure to show clearly the restricted domain and range of Amanda's function.
Since the domain of Amanda’s function is
, the range of Eric’s inverse function will be .
What is the range of Amanda’s function? How does this restrict the domain of Eric’s function which would otherwise look like a full parabola?