Given the function y=x^2-3/x^2+5x+6 choose th correct horizontal asymptote. none y=0 y=1 y=-2, y=-3

Given the function y=x^2-3/x^2+5x+6 choose th correct horizontal asymptote. none y=0 y=1 y=-2, y=-3

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  1. y = 1

    Step-by-step explanation:

    Given function is:

    [tex]\frac{x^2+8x+3}{x^2+3x+1}[/tex]

    In order to find the horizontal asymptote, the coefficients of highest degree variable of numerator and denominator are divided.

    In our case,

    both the numerator and denominator have 1 as he co-efficient of x^2

    So the horizontal asymptote is y = 1/1

    Hence, third option y=1 s correct ..

  2.  NONE

    Step-by-step explanation:

    Consider that m is the degree of the numerator and n is the degree of the denominator.

    The rules for horizontal asymptote (H.A.) are as follows:

    If m > n   then no H.A. (use long division to find the slant asymptote)

    If m = n   then H.A. is y = leading coefficient of numerator/leading coefficient of denominator

    If m < n   then H.A. is y = 0

    Given: g(x) = 5x⁵/(x³ - 2x + 1)

    --> m = 5, n = 3

    Since m > n then there is no H.A.

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