How do you graph #y=(x-5)/(x+1)# using asymptotes, intercepts, end behavior?
For the asymptote, we have vertical ones and horizontal ones.
For vertical ones, we look at the denominator and determine when it would be
Horizontal ones are determined by finding the ratio of the coefficient in front of highest exponential value of the numerator and denominator. The highest exponential value on the numerator is x, and its coefficient is 1. The highest exponential value on the denominator is x as well, with its coefficient being 1. So the horizontal asymptote would be
The y intercept is when x is zero. So the y intercept would be
The x intercept is when y is zero. When
You can determine the end behavior just by looking at the horizontal asymptote. The horizontal asymptote tells you where the y value is going towards, which is