# What is the horizontal asymptote of #f(x) = (x+1) / (x^2 +3x - 4)#?

##### 2 Answers

Jul 17, 2018

y=0

#### Explanation:

If the polynomial in the numerator is a lower degree than the denominator, the x-axis (y = 0) is the horizontal asymptote. The degree is the power of the x variable(s).

Jul 17, 2018

#### Explanation:

#"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+1/x^2)/(x^2/x^2+(3x)/x^2-4/x^2)=(1/x+1/x^2)/(1+3/x-4/x^2)#

#"as "xto+-oo,f(x)to(0+0)/(1+0-0)#

#rArry=0" is the asymptote"#

graph{(x+1)/(x^2+3x-4) [-10, 10, -5, 5]}