This week in math we learned about reciprocal linear functions. The first thing you do with reciprocal linear functions is graph the original function. The second step you do is finding invariant points, which are the part of the line that matches up with 1 and -1 on the y-axis. You would then find the vertical and horizontal asymptotes which are the lines that separate the invariant points, going right down the middle. You would then draw the hyperbola, and you must make sure that the line gets closer, and closer to the asymptotes, but never actually touches them.

For example, if you were given the function f(x)=x+3 then the reciprocal would be f^{-1}(x)=\frac{1}{x+3}. You would first graph the original function, then you would find the invariant points which are (-2,1) and (-4,-1). You would then put the vertical and horizontal asymptotes, and then draw the hyperbola. The picture bellow is of this example: