How do you find vertical, horizontal and oblique asymptotes for #f(x) = (3)/(5x)#?

1 Answer
Jun 14, 2016

Answer:

vertical asymptote x = 0
horizontal asymptote y = 0

Explanation:

Vertical asymptotes occur as the denominator of a rational function tends to zero. To find the equation set the denominator equal to zero.

solve 5x = 0 → x = 0 is the asymptote

Horizontal asymptotes occur as

#lim_(xto+-oo),f(x)toc" (a constant)"#

divide numerator/denominator by x

#(3/x)/((5x)/x)=(3/x)/5#

as #xto+-oo,f(x)to0/5#

#rArry=0" is the asymptote"#

Oblique asymptotes occur when the degree of the numerator > degree of the denominator. This is not the case here (numerator-degree 0, denominator-degree 1 )Hence there are no oblique asymptotes.
graph{3/(5x) [-10, 10, -5, 5]}