next we will introduce the finite or asymptotic and behavior limits as a part of the introduction we will discuss the definitions interpretations and a few examples we associate the following behavior resulting in a horizontal asymptote y equals l on the right side with the following limit statement called a finite or asymptotic end behavior limit note that we do not suggest that the graph must approach the asymptote in any particular way it can approach it from above or below either of these behaviors are described with the same limit statement and schematically can be expressed with an arrow aligning with the asymptote on the right side of the graph we say f approaches to l as x approaches to infinity from the left since it is only possible to approach positive infinity from the left frequently the phrase from the left is emitted so the statement simply reads as f approaches to l as x approaches to infinity also please note that the graph may or may not intersect the asymptote on the left side before the function expresses the asymptotic behavior we associate the following behavior resulting in a horizontal asymptote y equals l on the left side with the following limit statement called a finite or asymptotic end behavior limit note that we do not suggest that the graph must approach the asymptote in any particular way it can approach it from above or below and either of these behaviors are described with the same limit statement and schematically can be expressed with an arrow aligning with the horizontal asymptote on the left side of the graph we say f approaches to l as x approaches to negative infinity from the right since it is only possible to approach negative infinity from the right frequently the phrase from the right is immediate so the statement simply reads as f approaches to l as x approaches to negative infinity also please note that the graph may or may not intersect the asymptote on the right side before the function expresses the asymptotic behavior so to interpret the two-sided infinite limits we would first read it as f approaches to positive or negative infinity as x approaches 2 a from both sides next we would mark the asymptote x equals a on the coordinate plane and then draw the behavior according to the statement so to interpret the two-sided infinite limits we would first read it as f approaches to positive or negative infinity as x approaches 2 a from both sides next we would mark the asymptote x equals a on the coordinate plane and then draw the behavior according to the statement so to interpret the two-sided infinite limits we would first read it as f approaches to positive or negative infinity as x approaches 2 a from both sides next we would mark the asymptote x equals a on the coordinate plane and then draw the behavior according to the statement let's do an example consider a function defined by the following graph and let's find the following limits in other words let's describe the asymptotic end behavior of the graph to find this finite end behavior limit we need to determine the equation of the horizontal asymptote on the left as x approaches to negative infinity it is easy to see that the equation is y equals negative one in other words f approaches to negative one as x approaches to negative infinity therefore the answer is negative one similarly to find this finite end behavior limit we need to determine the equation of the horizontal asymptote on the right as x approaches to positive infinity it is easy to see that the equation is y equals 2. in other words f approaches to 2 as x approaches to positive infinity therefore the answer is 2. we discussed the definition of a finite or asymptotic and behavior limit using the graphing approach