Final Answer:
The equation of the vertical asymptote is x = a, where 'a' is the x-coordinate of the vertical asymptote.
Step-by-step explanation:
In a rational function, the vertical asymptote(s) occur where the denominator of the rational expression becomes zero. To find the equation of the vertical asymptote, set the denominator equal to zero and solve for 'x'.
Let's consider a rational function in the form f(x) = g(x) / h(x), where 'g(x)' and 'h(x)' are polynomials.
If h(x) = 0 at some value of 'x', then f(x) will have a vertical asymptote at that value. The equation of the vertical asymptote is x = a, where 'a' is the solution to h(x) = 0.
For example, if h(x) = (x - 2)(x + 3), then the vertical asymptotes would be x = 2 and x = -3 since h(x) becomes zero at those points.
Understanding the behavior of vertical asymptotes is crucial in analyzing the graph of a rational function. They represent values of 'x' where the function approaches infinity, and they can help identify the domain and range of the function.