Determine the slant asymptote for the function f(x)=3x^2-4x + 5/ x-3

y=3x+5

Step-by-step explanation:

To determine the slant asymptote you must perform polynomial division and also the degree of the numerator must be one greater than degree of the denominator for it to even exist.  (We do have that here by the way since degree of the top is 2 and the degree of the bottom is 1).

Let's begin the division process:

I'm using synthetic. You can also use long.

3 goes on the outside because we are dividing by x-3

3 |   3     -4      5

  |           9      15

    ----------------------

      3       5       20

So

So the slant aymptote is y=3x-5 since 20/(x-3) approaches 0 as x approaches  infinity.