Question

Number of asymptotes of the function, $f\left(x\right)=\frac{2x^2+5x-3}{x^2-2x}$ is

• A. $2$
• B. $1$
• C. $3$
• D. $4$

Answer 1

The correct option is C $3$

Given function is $f\left(x\right)=\frac{2x^2+5x+3}{x^2-2x}$

$f\left(x\right)$ does not exist if $x^2-2x=0$

$\Rightarrow x=0,2$

Therefore, $x=0$ and $x=2$ are asymptotes of $f\left(x\right)$

As $x\to \infty ,$ $f\left(x\right)\to 2$

Therefore, $f\left(x\right)=2$ is also asymptote of given function

Totally there are $3$ asymptotes for the given function.

Therefore, the correct option is $C$.