Question

Make up a rational function that has $y=2x+1$as an oblique asymptote. Explain the methodology that you used.

Short answer

The rational function$\frac{6x^2+x-1}{3x-1}$which is having$2x+1$as an oblique asymptote.

Step-by-step solution

Step 1 Let us assume a function,

$f\left(x\right)=\frac{a{x}^m+b{x}^{m-1}+....+k}{a_1{x}^p+b_1{x}^{p-1}+....+k_1}$

Let us multiply the given function by $\left(2x+1\right)$.

$\frac{a{x}^m+b{x}^{m-1}+....+k}{a_1{x}^p+b_1{x}^{p-1}+....+k_1}\left(2x+1\right)$

Step 2 So as the multiplied and divided polynomial can take any value.

So, let us take any function like $3x-1$after multiplication and division it will be as such $\frac{6x^2+x-1}{3x-1}$.

Hence this function can be taken as one of the polynomial function having $2x+1$as its oblique asymptote.