Reciprocal Functions

Reciprocal Functions is taking a function like y= 2+12x-20 and making it y=1/ (2+12x-20) is the functions reciprical.

When finding y= 2+12x-20 and its reciprical y=1/ (2+12x-20), you want to graph the original function first all the time. After you have graphed the original function, you have to find its vertical asymptote which is where the graph touches the x axis and where the reciprocal will never cross over. It acts like a dotted line on going vertically upwords to help you graph the reciprical. There is also a horizontal asymptote which is for now always on the a axis, it acts simular to the vertical asymptote except it sits vertically on the x axis making sure that your reciprical never touches it.

Once you have graph the parabola, now that you have found that there is no x intercept in the equation, so there is no vertical asymptote. This is what you would call a pimple graph, one that does not have a vertical asymptote but does however still have a horizontal asymptote. To find out where it recipricates you have to find the vertex on the graph.

(3,-2) now that the vertex is found, you can recipricate the vertex, but only the -2 or the y, then you get (3,-1/2) and then you draw the bump that carries on through the x axis and down towards the new vertex for the reciprocal function.