Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Get quick and reliable solutions to your questions from knowledgeable professionals on our comprehensive Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
Given:
The function is
[tex]f(x)=\dfrac{x^2-2x-2}{x-2}[/tex]
To find:
The vertical asymptote and oblique asymptote.
Solution:
We have,
[tex]f(x)=\dfrac{x^2-2x-2}{x-2}[/tex]
To find vertical asymptote, equate denominator equal to 0.
[tex]x-2=0[/tex]
[tex]x=2[/tex]
So, the vertical asymptote is [tex]x=2[/tex].
In the given function degree of numerator is greater than denominator so, their is an oblique asymptote. To find oblique asymptote divide the numerator by denominator.
Dividing [tex]x^2-2x-2[/tex] by [tex]x-2[/tex] using synthetic division, we get
2 | 1 -2 -2
2 0
--------------------------
1 0 -2
-------------------------
Here, starting elements of bottom row represent coefficient of quotient and last element of bottom row represents the remainder.
[tex]Quotient=x, Remainder=-2[/tex]
Since, quotient is x, therefore, the oblique asymptote is [tex]y=x[/tex].
Therefore, the correct option is B.
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.