Pearson Algebra 2 Common Core, 2011
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Pearson Algebra 2 Common Core, 2011 View details
2. The Reciprocal Function Family
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Exercise 47 Page 513

Consider the general equation of a reciprocal function.
Let's start by graphing the parent function to all reciprocal functions, This function has a constant of variation of and a horizontal and vertical asymptote of

Notice that the minimum distance from the origin to this function is a line from to or Let's add this to the graph.

If we zoom in on one of the quadrants, we notice that the distance is the hypotenuse of a triangle. In such a triangle the hypotenuse is always longer than any of the legs. Since the legs are both unit long, the hypotenuse must be units.

As we can see, when the constant of variation is the function passes through If we can push this graph outward so that the closest point to the origin is we will have a reciprocal function with a minimum distance of units. This is because this point creates a triangle with a leg length of

To determine the function we should substitute the known point and solve for
Solve for
One function is By placing a negative sign before we get a second function with the same characteristics.