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

Answer:

Oblique asymptote at y = 3x+14

Step-by-step explanation:

$f(x)= \frac{3x^2+2x-5}{x-4}$

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