Question

What is the equation of the slant asymptote of the function?

f(x)=4x³+9x²+x−5 / x²+ 3
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Answer 1

To find the slant asymptote of the function f(x) = (4x³ + 9x² + x − 5) / (x² + 3), use polynomial long division. The quotient of the division gives the slant asymptote, which in this case is y = 4x.

Step-by-step explanation:

The equation of the slant asymptote of the function f(x) = (4x³ + 9x² + x − 5) / (x² + 3) can be found by performing polynomial long division.

1. Divide the leading term of the numerator (4x³) by the leading term of the denominator (x²) to get 4x.
2. Multiply the entire denominator (x² + 3) by 4x and subtract the result from the numerator.
3. The result of the subtraction will be a new polynomial with degree less than the denominator, which is then ignored for the asymptote.
4. The quotient from the long division process (in this case, 4x) is the equation for the slant asymptote.

Therefore, the equation of the slant asymptote for this function is y = 4x.