This week in PreCalc 11 we learned about graphing the absolute value of a linear and quadratic function and the reciprocal of them. I will be focusing on the reciprocal form of linear equations, the first thing you do for it is graph the parent function. Next I would find the invariant points, then find the asymptotes, then draw the hyperbola’s.
Then you would find the invariant points by using 1 and -1 the look along the x line and find where it hit’s the parent line then that’s your invariant points. Ex: the green and blue lines represent where they are.
Then we have to find the x and y asymptotes, most of the time the x intercept is the y asymptote and then 0 is the x asymptote. Ex: the blue line represents the y asymptote and the green line represents the x asymptote.
Then lastly we just have to draw the hyperbola’s by using those lines as a guideline. Ex: