How to Find the Vertical Asymptote
Finding the vertical asymtote is the easiest at of all them. Yes! Don't make a big deal out of it it's simple.
To locate the vertical asymtote of any given rational function factor out the denominator to it's lowest form. Set the denominator set to zero and solve for the given value. This is where your vertical asymtote is located.
Remember vertical asymtotes are always VERTICAL that means you dont need to have a y value all you need is an x locaiton and create a vertical line at that point.
Typically vertical asymptotes are written with a vertical dashed line.
Steps to follow
- Factor numerator and denominator
- Cancel any similar terms
- Set the denominator to zere and solve
Example:
$$\frac { 4x }{ { x }^{ 2 }+4x+4 }$$
$$\frac { 4x }{ { (x+2) }^{ 2 } }$$
$$x+2=0$$ $$x=-2$$ $$VA=-2$$