This week in Pre Calc 11 we learned how to graph Reciprocal Value Functions. A function is reciprocated when the values are flipped, for example the reciprocal of is because the values flipped. In order to graph reciprocal linear functions we must first graph the parent function. Next we will be able to find the horizontal and the vertical asymptotes. In grade 11, the horizontal asymptote will always be drawn along the x-axis, which means the equation for our horizontal asymptote is To determine where the vertical asymptote will be, we must find where our parent function intersects the x-axis, which will be our x-intercept and draw a vertical line through it. This line will be our vertical asymptote, represented by and it’s equation is Once we have determined our asymptotes, we now must find the invariant points. The invariant points are are determined by where the parents function crosses the numbers and on the y-axis. We are now able to graph our reciprocal linear functions by starting at the invariant points and drawing two hyperbola’s that follow along the horizontal and vertical asymptotes, gradually getting closer to them, but never actually touching them.

An example of how to graph a reciprocal linear function is

The first step is to graph the parent function which is is has a slope of and it’s y-intercept is

Next we must find the verical and the horizontal asymptotes. Which will be and because as we can see in the graph, the x-intercept of the parent function is Next we must find the invariant points which will be and Finally, we are able to draw our two hyperbola’s.