How do you find the vertical, horizontal and slant asymptotes of: #f(x)=(x+1)/(2x+10)#?

1 Answer
Jan 14, 2017

Answer:

The curve is a rectangular hyperbola.
Horizontal asymptote : #larr y = 1/2 rarr#
Vertical asymptote : #uarr x= -5 darr#

Explanation:

An equation in the form

#(y-m_1x-c_1)(y-m_2x-c_2)=c ne 0# represents a hyperbola

contained between the asymptotes

#(y-m_1x-c_1)(y-m_2x-c_2)=0#

Here, cross multiplying and rearranging,

#(2y-1)(x+5)=6#

The asymptotes at right angles are

#2y-1)(x+5)=0, giving

#x=-5 and y = 1/2#

Now, see the asymptotes-inclusive graph.

graph{((2y-1)(x+5)-6)(2y-1)(x+.000000001y+5)=0 [-15, 5, -7.5, 7.5]}