Explain how to find the equation of the vertical asymptotes of a reciprocal function in full details.

* Steve told me to look up in the web, and did, but still i couldn't find the correct one. someone help please....

To find the equation of the vertical asymptotes of a reciprocal function, you can follow these steps:

Step 1: Start with the equation of the reciprocal function in the form f(x) = 1/g(x), where g(x) is a function that represents the numerator or denominator of the reciprocal function.

Step 2: Set the denominator, g(x), equal to zero and solve for x. This will give you the values of x where the reciprocal function is undefined or where there may be vertical asymptotes.

Step 3: Since vertical asymptotes occur when the value of x approaches these undefined or discontinuous points, the equation of the vertical asymptote(s) will be in the form x = a, where 'a' is a constant value that corresponds to the x-values obtained in step 2.

Let's illustrate this process with an example.

Example: Find the equation of the vertical asymptotes for the function f(x) = 1/(x squared - 4).

Step 1: The function is already given in the form f(x) = 1/g(x), where g(x) = x^2 - 4.

Step 2: Set the denominator, g(x) = x^2 - 4, equal to zero and solve for x:
x^2 - 4 = 0

By factoring, we obtain:
(x + 2)(x - 2) = 0

Solving for x, we find two possible values: x = -2 and x = 2.

Step 3: The equation of the vertical asymptotes will be in the form x = a, where 'a' corresponds to the potential values obtained in step 2. Thus, the equations of the vertical asymptotes for the function f(x) = 1/(x^2 - 4) are x = -2 and x = 2.

Note that when graphing this function, we would draw vertical lines at x = -2 and x = 2, as they represent the vertical asymptotes.