k(x)= 2x+1/ x-9 [[[--]](5.) p(x)= 2x^2+3 / (x-1.5)^2 {[[--}} 6.) m(x)= 3x-8/x^2-7?

Question

Identify all vertical and hoirizontal asymptotes of the graph of each rational function

Answer 1

to find vertical asymptotes just put bottom part of fraction equal to zero and solve for x, and for horizontal if the degree of the top is more than on the bottom, then there is none, if its the same then its y=1 and if its less its y=0, degree is the highest exponent.

4. x=9, y=1
5. x=1.5, y=1
6. x=+-sqrt 7, x=0

Answer 2

set the denominator of each rational function equal to zero and solve. these will be the vertical asymptotes

the rules for horizontal asymptotes are as follows:

if the degree of the numerator is greater than the degree of denominator by an integer other than 1 then there is no horizontal asymptote

if the degree of the denominator is greater than the degree of the numerator then there is a horizontal asymptote at y=0

if the degree of the numerator is equal to the degree of the denominator then divide the two terms of highest degree in both the numberator and denominator and you will have the answer

if the degree of the numerator is greater than the degree of the denominator by one then you divide the numerator by the denominator and throw out the remainder. the linear equation is called a slant asymptote of the rational function

Answer 3

k(x) has horizontal asymptote y=2 and vertical asymptote x=9

p(x) has horizontal asymptote y=2 and vertical asymptote x=1.5

m(x) has horizontal asymptote y=0 and vertical asymptote x=+/-sqrt(7)

Answer 4

wait a minute is this all one question or 3? there gotta be some clean up with the symbols.
k(x) HA is 2 VA is 9
p(x) HA is 2 VA is 1.5
m(x) HA is none VA is radical 7

Answer 5

For vertical, denominator=0
For hoirizontal lim f(x), x-----> ∞

k(x)
vertical: x=9
horizontal: y=2

p(x)
vertical: x=1.5
horizontal: y=2

m(x)
vertical: +- sqrt 7
horizontal: y=0