Week 13 – Math 11

This week in math 11 we learned about reciprocal functions. These are hyperbolas created from a linear equation. Some important things to remember about these are the vertices and horizontal asymptotes and invariant points. The asymptotes are lines that the hyperbola will come very close to touching but never will, and the invariant points are -1 and 1 because the are the inly numbers that even when reciprocated stay the same.

For example if you were given the equation y=2x+1 and were asked to graph both the original equation and the reciprocal equation y=\frac{1}{2x+1} this is how it would work. First you would graph y=2x+1 then you would go to the centre of the graph (0,0) and go up to 1, from here you are either going to go right or left depending on which way will allow you to bump into your line (keep in mind this point may not be a nice number). In this case 1 in our y intercept. Then you are going to go down to -1 and do the same thing. Next you are going to want to find you vertical and horizontal asymptotes, for math 11 the horizontal asymptote will always be y=0 (meaning it goes right along the x axis) now you are going to want to find the vertical one and this can be done by solving to find the x intercept of the linear equation. For this the vertical asymptote is x=\frac{-1}{2}. Now that those are figured out you draw curved lines that doesn’t touch any of the asymptotes but get very close.

*A reciprocal function in the equation flipped. You have to remember that the equation y=2x+1 is a fraction and is over 1 (y=\frac{2x+1}{1}), the reciprocal would be y=\frac{1}{2x+1}

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