This week in pre-calc, we learned how to the reciprocals of linear functions. A reciprocal is when you have 2 hyperbolas that are reflections of each other. So if you divide the graph in a slanted direction, you get a reflection of the 2 hyperbolas, one in the positive quadrants and one in the negative quadrants.
The equation for graphing the reciprocal of a linear equation is 1/x+1 (you just take your linear equation and put it over 1.
The first step when graphing the reciprocal of a linear function is to draw out the original linear function. Once you have your line, the second step is to go to 1 and -1 on your y-axis. When you get to 1 and -1, you go across on the x-axis and find the points where the linear equation lines up with 1 and -1.
After you find where they intersect, you can draw a line that is equal distance between the point at -1 and 1 to get your vertical asymptote. This is acting as a magnetic field or a boundary that you cannot cross. It’s acting as your ‘0’ value. Your horizontal asymptote will be ‘0’ overtime for what we’re learning. This means that when you’re graphing your reciprocals, you will not be able to cross over the horizontal and vertical asymptotes. You always get closer and closer to reaching ‘0’ but you will never reach ‘0’ when graphing reciprocals.
