Question

Give the equations of any vet f(x)=(3)/(x-5)

Answer 1

`\[f(x) = (3)/(x-5)\]`

The equation represents a rational function with a vertical asymptote at (x = 5), and understanding its characteristics is essential for analyzing its behavior.

Step-by-step explanation:

The given equation represents a rational function, where f(x) is defined as the constant 3 divided by the quantity (x-5). In this function, the numerator is a constant value (3), and the denominator is a linear expression (x-5).

The expression (x-5) in the denominator indicates that the function is undefined when (x) is equal to 5, as division by zero is not allowed. Therefore, the function has a vertical asymptote at (x = 5).

Rational functions like this one often exhibit specific characteristics, such as asymptotes, intercepts, and behavior as (x) approaches positive or negative infinity. Understanding these features is crucial for analyzing the behavior of the function across different values of (x).