# What are the asymptotes of #f(x)=-x/((2x-3)(x-7)) #?

##### 1 Answer

Apr 28, 2017

#### Explanation:

The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the values that x cannot be and if the numerator is non-zero for these values then they are vertical asymptotes.

#"solve " (2x-3)(x-7)=0#

#rArrx=3/2" and " x=7" are the asymptotes"# Horizontal asymptotes occur as

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

divide terms on numerator/denominator by the highest power of x, that is

#x^2#

#f(x)=-(x/x^2)/((2x^2)/x^2-(17x)/x^2+(21)/x^2)=-(1/x)/(2-17/x+(21)/x^2# as

#xto+-oo,f(x)to-0/(2-0+0)#

#rArry=0" is the asymptote"#

graph{-(x)/((2x-3)(x-7)) [-10, 10, -5, 5]}