An example of a graph of a reciprocal function looks like this http://wpcontent.answcdn.com/wikipedia/commons/thumb/2/29/Rectangular_hyperbola.svg/330px-Rectangular_hyperbola.svg.png
To find the reciprocal of a graph, you would take the original equation ex. y=2x+2 and inverse the "x" side of the equation so it becomes y=1/2x+2
After this set up a table of values for the y and x and the 1/y so that you can plot the original graph points and than its reciprocal function points.
After setting up table of values, solve for variant points by setting value of y to 1 and -1 and solving for x on both of your new equations.
Ex.) y=2x+1
1=2x+1 --> 0=2x --> x=0 y=1 (invariant point)
-1=2x+1 --> -2=2x --> x= -1, y= -1 (invariant point)
The invariant point is to see where the line of the graph will start to turn so it's acting as a turning point for the line.
After plotting invariant points and setting up table of values all thats left to do is plot the reciprocal graph
Make sure to label horizontal and vertical asymptotes and draw arrowheads for both lines, because as a function the line continues outside of the graph.
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ReplyDeleteHi Judd, you did a nice job of summarizing the steps to drawing the reciprocal graph. I like that you showed how to find the invariant points. These are points that do not change from the original graph. I also like that in your last line you stressed the importance of drawing the asymptotes and putting on arrow heads. Thanks for the summary.
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