Which statement is true about the asymptotes of a rational function if the degree of the polynomial function in the numerator is 1 and the degree of the polynomial function in the denominator is 2?
a) it has two horizontal asymptotes
b) it has only one vertical asymptote
c) it has only one horizontal asymptote
d) it has no vertical asymptote
e) it has no horizontal asymptote

answer:

it has only one horizontal asymptote

step-by-step explanation:

the asymptotes of a rational function if the degree of the polynomial function in the numerator is 1 and the degree of the polynomial function in the denominator is 2

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

here the degree of numerator is 1   and the degree of denominator is 2

1 < 2 so horizontal asymptote at y=0

it has only one horizontal asymptote

vertical asymptote depends on the degree of denominator

denominator degree is 2, so it has one or two vertical asymptotes

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0