Question

What is the graph of the function f(x) = the quantity of negative x squared minus 2 x minus 2, all over x minus 2?

Group of answer choices

graph with vertical asymptote of x equals negative 2, and oblique asymptote of y equals negative x

graph with vertical asymptote of x equals 2, and oblique asymptote of y equals x

graph with vertical asymptote of x equals 2, and oblique asymptote of y equals negative x minus 4

graph with vertical asymptote of x equals 5, and oblique asymptote of y equals negative x minus 4

Answer 1

Given:

The function is

`f(x)=(x^2-2x-2)/(x-2)`

To find:

The vertical asymptote and oblique asymptote.

Solution:

We have,

`f(x)=(x^2-2x-2)/(x-2)`

To find vertical asymptote, equate denominator equal to 0.

`x-2=0`

`x=2`

So, the vertical asymptote is
`x=2`.

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
`x^2-2x-2` by
`x-2` 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.

`Quotient=x, Remainder=-2`

Since, quotient is x, therefore, the oblique asymptote is
`y=x`.

Therefore, the correct option is B.