# Do all functions with vertical asymptotes also have oblique asymptotes? I just started learning about asymptotes in my Advanced Functions class, and as I was taking a look at all this stuff, a question came up. Do all rational functions that have vertical asymptotes also have an oblique asymptote? Or is an oblique asymptote only formed when the degree of the numerator is 1 higher than the degree of the denominator, and so only functions with a vertical asymptote with a degree of 1 can also have an oblique asymptote?

Do all functions with vertical asymptotes also have oblique asymptotes?
I just started learning about asymptotes in my Advanced Functions class, and as I was taking a look at all this stuff, a question came up. Do all rational functions that have vertical asymptotes also have an oblique asymptote? Or is an oblique asymptote only formed when the degree of the numerator is 1 higher than the degree of the denominator, and so only functions with a vertical asymptote with a degree of 1 can also have an oblique asymptote?
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Shania Delacruz
You are dealing with dividing two functions and the bottom function approaches zero while the top function approaches a non zero value.
For example
$f\left(x\right)=\frac{2x+1}{\left(x-5\right)\left(2x+3\right)}$
where x=5 and x=−3/2 are vertical asymptotes.
Oblique asymptotes happen when your function behaves like a non-horizontal straight line as x goes to $\mathrm{\infty }$ or $-\mathrm{\infty }$ We find slant asymptotes by dividing the top by the bottom and ignoring the remainder.
For example
$f\left(x\right)=\frac{2{x}^{2}+1}{2x+3}$
$g\left(x\right)=x-3/2$
which is a straight line.
A function may have both vertical and oblique asymptote but not both horizontal and slant.