To find the equation of a vertical asymptote, you need to identify the values of x that make the function undefined. These values typically occur when you have a rational function, where the denominator equals zero.
Here are the steps to follow:
- Identify the function: Start with the function you are working with, particularly if it’s a rational function in the form of f(x) = P(x) / Q(x), where P and Q are polynomials.
- Set the denominator to zero: To find the vertical asymptote, set the denominator Q(x) equal to zero. This gives you the values of x that make the function undefined.
- Solve for x: Solve the equation Q(x) = 0 to determine the specific x-values. Each of these x-values corresponds to a vertical asymptote.
- Write the equation: Write the equations of the vertical asymptotes in the form x = a, where a is any value you found from the previous step.
For example, for the function f(x) = 1 / (x – 3), you would set the denominator x – 3 = 0, which solves to x = 3. Thus, the equation of the vertical asymptote is x = 3.
Keep in mind that vertical asymptotes indicate the behavior of the graph as it approaches the asymptote but never actually touches it. Understanding and identifying these asymptotes is crucial for better graphing and analyzing functions.