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

1 Answer
Lucy
Jul 10, 2018

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#

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