From the set of five sketches, select all the relations that are functions. Give a brief reason using the vertical line test.

From those that are functions, select any one that is not one-to-one and explain why using the horizontal line test.

For one graph that is a one-to-one function, state its domain and range as suggested by the sketch and describe how the graph of its inverse would relate to it. No sketch required.

Find the equation of the normal to $y = x^2$ at $A(1, 1)$.

The normal meets the parabola again at $B$. Find the coordinates of $B$.

Let $\theta$ be the angle $A\hat{O}B$ (the angle between $OA$ and $OB$). Show that $\tan \theta = 5$.