Reciprocal Function
The reciprocal function, denoted as f(x) = 1/x, is an important mathematical concept in algebra and calculus
The reciprocal function, denoted as f(x) = 1/x, is an important mathematical concept in algebra and calculus. It is also known as the multiplicative inverse because it is the number you multiply by to get 1.
The reciprocal function has certain properties worth noting:
1. Domain: The domain of the reciprocal function is all real numbers except 0. This is because division by zero is undefined.
2. Range: The range of the reciprocal function is also all real numbers except 0. As you approach positive or negative infinity on the x-axis, the function approaches zero, which means the reciprocal gets larger and larger in magnitude. However, it never actually reaches zero, as dividing any number by zero is undefined.
3. Vertical Asymptotes: The reciprocal function has two vertical asymptotes at x = 0. This means that the graph of the reciprocal function approaches positive infinity as x approaches 0 from the positive side, and approaches negative infinity as x approaches 0 from the negative side.
4. Horizontal Asymptote: The reciprocal function has a horizontal asymptote at y = 0. This means that as x approaches positive or negative infinity, the function gets closer and closer to zero.
5. Graph: The graph of the reciprocal function is a hyperbola. It is symmetric with respect to the line y = x, and it has two branches that approach the asymptotes as x moves farther away from 0.
To graph the reciprocal function, you can evaluate different x values and calculate the corresponding y values using the formula f(x) = 1/x. Plot these points on a coordinate plane and connect them to obtain the graph of the function. Remember to exclude the point (0,0) from the graph since division by zero is undefined.
It is also important to note that the reciprocal function is commonly used in solving equations involving rational expressions. By taking the reciprocal of both sides of the equation, you can simplify the expression and solve for the variable.
That is a brief overview of the reciprocal function. If you have any specific questions or require further clarification, please let me know!
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