Question

What is the equation of the oblique asymptote? 2 h(x)=x²-x-2 x+1 O A. y=x+1 O B. y=x2+1 O c. y=x-2 O D.y=x

Answer 1

Explanations:

To get the equation of the oblique asymptote of a function, we will first have to get the quotient of the given function. Given the function:

`h(x)=(x^2-x-2)/(x+1)`

Factoring the numerator and simplifying will give;

`\begin{gathered} h(x)=(x^2-2x+x-2)/(x+1) \\ h(x)=((x^2-2x)+(x-2))/(x+1) \\ h(x)=(x(x-2)+1(x-2))/(x+1) \\ h(x)=\frac{\cancel{(x+1)}(x-2)}{\cancel{x+1}} \\ h(x)=x-2 \end{gathered}`

The equation of the oblique asymptote is the first two terms of the quotient that is x - 2