MATH 112 Lecture Notes - Lecture 19: Asymptote
2 Nov 2017
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Why x can not cross over -1. if we plug in a value that is very close to -1 such as 0. 999999. the denominator is. 1-0. 999999=0. 000001 which means the numerator times 1000000 which is a big number. So when x approaches -1, the y value will approach infinity. )(1 the x can not cross over -1,2,-16. End behavior: the degree of the numerator is smaller than the degree of the denominator, so the end behavior is y goes to zero. Plug in a big positive x value, the y is positive. Plug in a small negative value, the y is negative. So the right side of the graph is above the x-axis. The left side of the graph is below the x-axis. When x goes to infinity, both the numerator and denominator go to infinity, so why the y value is zero. The reason is the denominator goes to infinity faster than the numerator.
