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

Answer 1

Below

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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Answer 2

Benjamin Achtenberg

To find the slant asymptote of the function ( f(x) = \frac{3x^2 + 2x - 5}{x - 4} ), you need to perform polynomial long division or synthetic division to divide the numerator polynomial by the denominator polynomial. After dividing, the quotient obtained will represent the equation of the slant asymptote.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.