Rational Functions

1. Intercepts (X,Y)

1.1. X intercept:

1.1.1. The zeros of the numerator are the x intercepts as long that they are not excluded values

1.2. Y intercept:

1.2.1. To find the y intercept just plug 0 in x and we find our y intercept

2. Asymptotes

2.1. asymptotes are the surrounding of my function, they affect the function, but they are not the function.

2.1.1. Vertical asymptotes

2.1.1.1. are vertical lines which correspond to the zeroes of the denominator of a rational function

2.1.1.1.1. The excluded values that does not cancel are the vertical asymptotes

2.1.2. Horizontal asymptotes

2.1.2.1. If the degree of the denominator is higher than the degree of the numerator, the asymptote is horizontal therefore y=0.

2.1.2.1.1. If it is the same, it is horizontal, and to get its value, the leading coefficients are divided

2.1.3. Slanted asymptotes

2.1.3.1. If the degree of the numerator is higher than the degree of the denominator, the asymptote is a slant. If it is even it is a positive slant, if it is odd it is a negative slant.

2.1.3.1.1. To find the slant asymptote you must divide the numerator by the denominator using either long division or synthetic division.

3. Holes

3.1. Holes: repeat on the numerator and denominator

3.1.1. The whole marks the place where the values in the fraction cancel. So the cancelled values and the excluded values are the holes.