y = 1/x
The equation y = 1/x represents a mathematical relation between two variables, y and x
The equation y = 1/x represents a mathematical relation between two variables, y and x. In this case, y is equal to the reciprocal of x.
To understand this equation graphically, we can plot the points that satisfy the equation on a coordinate grid. We can choose different values for x and calculate the corresponding values for y.
For example, let’s choose x = -2, -1, 0, 1, and 2:
When x = -2, y = 1/(-2) = -1/2
When x = -1, y = 1/(-1) = -1
When x = 0, y is undefined because it involves division by zero (division by zero is undefined in mathematics).
When x = 1, y = 1/1 = 1
When x = 2, y = 1/2 = 1/2
Plotting these points on a graph, we get the following:
|
|
-1/2 |
——–+—–
|
|
-1 |
——–+—–
|
|
1 |
——–+—–
|
|
1/2 |
——–+—–
|
From the graph, we can observe that the relation y = 1/x forms a hyperbola. As x approaches positive or negative infinity, y approaches zero. As x approaches zero, y approaches positive or negative infinity depending on the sign of x.
Furthermore, we can notice that the graph is symmetric about the line y = x, meaning that if we reflected the right side of the graph onto the left side, we would get a perfect match.
This mathematical relation has various applications in fields such as physics, engineering, and finance. For example, it can be used to model the relationship between resistance and conductance in electrical circuits or the inverse relationship between price and demand in economics.
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