Reciprocal functions are actually extremely important. Isaac Newton deduced that the forces needed to hold planets in orbits is a reciprocal relationship with the squares of their distances. Radioactive isotopes decay reciprocally, and trees lose their leaves reciprocally.
The graph appears to split into two parts. As x gets really close to 0, y would be very large. And when for x is 0, you cannot divide by 0. There is no value. The graph also gets closer and closer to the y-axis, but never touches it for the same reasons. This is why reciprocal graphs have two separate parts, and bend towards a horizontal and vertical line that they never quite touch.
The shape always stays the same - but the graph could sometimes be shifted or a negative reciprocal is a reflection of the positive reciprocal.
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