Question

What is the oblique asymptote of the function f(x) = the quantity x squared plus 5x plus 6 over the quantity x minus 4?

y = x + 9
y = x − 9
y = x + 1
y = x − 1

Answer 1

oblique asymptote y = x+9

i took the test

Answer 2

Answer y = x+9

Given function f(x) =
`(x^2+5x+6)/(x-4)`

To find out oblique asymptote we use long division

We divide x^2 + 5x + 6 by x-4

Hereby attached a file that shows long division

Long division steps are given below

1. Divide the first term of both numerator by denominator (x^2/x = x)

2. Multiply the answer x with x-4 that gives x^2 - 4x and put it at the bottom

3. Change the sign and subtract it

4. Repeat the step 1,2,3 till we get the remainder

We got quotient is x+9

So we write oblique asymptote y = x+9