Unit G Summary Questions #7: Vertical Asymptote & Limit Notation

7. Describe how we write limit notation for vertical asymptotes and what the notation means.

The limit notation for vertical asymptotes is written:

• As x--> # +, f(x)-->___
• As x --># -, f(x)-->___

The number that goes in As x-->___ is derived from the equation of a vertical asymptote after solving for it. If we had the equation be x=3 then we would write it as As x-->3+...The plus sign means "from the right side" meaning that when we look at the graph in our equation we look at the direction the graph is going from the right side of the vertical asymptote. If it is going down then f(x) would be approaching negative infinity. The negative sign means "from the left side" meaning that when we look at the graph in the calculator we also look at the direction the graph is going from the left side of the vertical asymptote. If we see that it is going up then we would write that f(x) is approaching infinity. We then put all of this together to write the limit notation. Example: As x-->3+, f(x)-->-∞ and As x-->3- , f(x)-->∞.  It is read as x approaches the right side of x=3, f(x) is approaching negative infinity and as x approaches the left side of x=3, f(x) is approaching infinity. The limit notation is just letting us know the direction of the graph on both sides of the vertical asymptote. If more than one equation exists for the vertical asymptotes then we create limit notation for all of the equations.