1. Graph the parabola . Then find the domain and range of .
2. Graph the parabola . Then find the domain and range of .
This means the parabola equals 0 at x=1 and x=0 (this should help graph it). A graph shows that between x=1 and x=0 y is positive.
Stationary point: .
The stationary point (it's a maximum, you can prove that part) is . This is the second part of the graph and comes in handy later!
The transformation is but we know that . Hence the transformation is .
The domain therefore is (otherwise we would have the square root of something negative).
The range is .