Age 14 to 18 Challenge Level:
Sketch the graphof $y=x^2$. If you exchange $x$ and $y$ the point
$(a,b)$ on one graph has an image $(b,a)$ on the other graph. What
transformation of the graphs will have this effect? What do you
expect the graph of $x= y^2$ to look like? Find these two graphs on
Now use a graphic calculator, or graphing software, to sketch the
two graphs. Were your predictions correct?
Find the other equations by considering the transformations of the
graphs, changing the equations accordingly and testing your
decisions by sketching the graphs and seeing if they match the
graphs in the illustration in the way that you expected.