Question

How do you find the slant asymptote of `f(x) = (3x^2 + 2x - 5)/(x - 4)`?

Answer 1

Below

Explanation:

When you notice that the degree of your numerator is greater than your denominator, then it is likely that you will need to use long division.

`f(x)=(3x^2+2x-5)/(x-4)=((x-4)(3x+14)+51)/(x-4)=(3x+14)+51/(x-4)`

To find your slant or oblique asymptote, you are finding what happens when x approaches infinity.

When x approaches infinity in the above equation, `51/(x-4)` will approach zero (try putting big numbers into your calculator)

Hence, `f(x)` becomes `3x+14+0=3x+14`
Therefore, your slant asymptote is `y=3x+14`