Suppose that $x =\frac { 1 } { t ^ { 2 } + 1 }$ and $y = t^{2}$ with $−∞ ≤ t ≤ ∞$.

1. Express $x$ as a function of $y$.

   Answer (a):

   $\textit{x}=\frac{1}{\textit{y}+1}$

2. Express $y$ as a function of $x$.

   Hint (b):

   Rewrite the answer from part (a) in $y =$ form.

3. How would the graph be different if we had $x = \frac { 1 } { u + 1 }$ and $y = u$ with $−∞ ≤ u ≤ ∞$?

   Hint (c):

   How are the range values of $y = x$ and $y = x^2$ different?