The graph of the equation y = 1/x is a hyperbola that has two distinct branches. This equation describes an inverse relationship between the variables x and y, meaning as x increases, y decreases, and vice versa.
When you plot this function, you’ll notice the following key features:
- Asymptotes: There are two asymptotes for this graph: the vertical line at x = 0 (the y-axis) and the horizontal line at y = 0 (the x-axis). The graph will never touch or cross these lines.
- Quadrants: The graph appears in the first and third quadrants of the Cartesian plane. In the first quadrant, both x and y are positive, while in the third quadrant, both are negative.
- Behavior: As x approaches 0 from the positive side, y increases towards infinity. Conversely, as x approaches 0 from the negative side, y decreases towards negative infinity.
This function can be useful in various fields such as physics, economics, and engineering, where inverse relationships are commonly observed.