Amanda wants to showcase her favorite function:
What is Eric's equation for his function e(x)?
What happens if the two machines are pushed together? What is e(f(−4))? Explain why this happens.
If f(x) and e(x) are graphed on the same set of axes, what would be true about the two graphs?
Draw the two graphs on the same set of axes. Be sure to show clearly the restricted domain and range of Amanda's function.
e(x) = (x − 1)2 − 5
Try several values for x in e(f(x)). x = −4 is a very convenient value to use. So are x = 4 and x = −1.
What happens in each case?
What characteristic has been common to all function-inverse pairs that you have graphed before?
Since the domain of Amanda’s function is x > −5, the range of Eric’s inverse function will be y > −5.
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?