Question

Identify the oblique asymptote of f(x) = quantity 3 x squared plus 2x minus 5 over quantity x minus 4.

Answer 1

f(x)=(3x^2+2x-5)/(x-4)
f(x)=(3x+5)(x-1)/(x-4)
x-4|(3x^2+2x-5)
(x-4)3x
3x^2+2x-5-(3x^2-12x)
(x-4)3x+14
14x-5-(14x-56)
51
Oblique=3x+14

Answer 2

Oblique asymptote at y = 3x+14

Explanation:

`f(x)= (3x^2+2x-5)/(x-4)`

The degree of numerator is 2

degree of denominator is 1

When the degree of numerator is greater than the degree of denominator by 1 then there is a slant asymptote

To find slant asymptote we divide by long division

3x +14

-------------------------------

x-4 3x^2+ 2x -5

3x^2-12x

---------------------------- (subtract)

+14x - 5

14x - 56

-------------------------------(subtract)

51

Oblique asymptote at y = 3x+14