unit 3 summer 2018

Question 1

rational function

Answer 1

for any two polynomials, their quotient is called a rational function

Question 2

domain of rational function

Answer 2

domain is all real numbers except the roots (zeroes) of the polynomial function of the denominator

Question 3

x-intercept of rational function

Answer 3

zeroes of the numerator but not the denominator

Question 4

y intercept

Answer 4

occurs at f(0)

Question 5

vertical asymptote

Answer 5

zeroes of the denominator but not of the numerator!

Question 6

continuity

Answer 6

there are breaks in rational functions when the function is not defined AKA the zeroes of the denominator

Question 7

holes

Answer 7

when something is a factor of both polynomials in numerator and denominator, there is a hole at that point.

there is only a hole if the order of the root is equal or greater than that of the denominator one. if not, it is a vertical asymptote

Question 8

horizontal asymptote

Answer 8

if degree of numerator is less than the denominator, then the asymptote occurs at y=0

if degree is equal of nermator and denominator, then the coefficient of the numerator over the denominator is the horizontal asymptote

if the degree on the bottom is lower, then there is no horizontal asymptote