Question

Find the equation of the slant asymptote of the function .

Question 8 options:

A)

y = x + 4

B)

y = x + 2.

C)

y = x – 2

D)

y = 0.

Answer 1

A rational function f with a slant asymptote y=x+4, a vertical asymptote at x=5, and one of the zeros at x=2 is f(x) = x^2 + 2x -8/x-5

Calculations and Parameters:

For the vertical asymptote, the denominator must contain (x−5) and for zeros, the numerator must contain (x−2)

So far f(x)= x−2/x-5

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Hence, for the slant asymptote, the quotient of the numerator divided by the denominator must be (x+4)

Therefore:

f(x)= (x+4)(x−2)/x−5

So f(x) = x^2 + 2x -8/x-5

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