unit 7 quiz 2 accel algebra II

vertical asymptotes

created by the factors in the denominator after simplifying the fraction ex: x=-3

holes

created by factors that reduce(cancel) from the numerator and denominator sub in the x coordinate into the simplified rational equation

domain

all real numbers except for excluded values: vertical asymptote and holes (x coordinates) if the original expression

horizontal asymptote: if degree of numerator equals degree of denominator

divide leading coefficients y= number other than 0

horizontal asymptote: if numerator degree > denominator degree

NO HORIZONTAL ASYMPTOTE: slant asymptote possible if n is 1 greater than d

horizontal asymptote: denominator degree > numerator degree

y=0: n<d

y intercept

constant in numerator divided by constant in denominator

x intercepts

created by factors in numerator that DON’T cancel out

slant asymptote

happens if numerator is 1 greater than denominator: polynomial division long or synthetic finds the equation of the lines, once you get the final answer the first LINEAR part is your slant asymptote. don’t include the remainder