Question:

Given y =[(x^2 - 3)(x + 2)^2] / [(x - 3)(x + 1)(4x^2 + 3)]?

by  |  earlier

0 LIKES UnLike

Identify:a)any vertical asymptote b)any horizontal asymptote c)x-intercepts d)y-intercepts

 Tags:

   Report

1 ANSWERS


  1. As the denominator approaches zero, the magnitude of y will approach infinity.  When y becomes undefined, that is where the vertical asymptote will be.

    So, a vertical asymptote is x = a, where a is a solution to the equation (x - 3)(x + 1)(4x^2 + 3) = 0.

    There are two real solutions: x = 3, x = -1.

    As x approaches positive or negative infinity, if the value of y approaches a constant, there is a horizontal asymptote.

    Since the smaller terms become insignificant as the magnitude of x approaches infinity, only the highest power term matters.  In this case, that is the fourth power of x. From the numerator, we have x^4, and, from the denominator, we have 4x^4.

    Since the powers are equal, there will be an asymptote.  Since the powers are even, the asymptote will be the same in either direction.

    y = x^4 / 4x^4 = 1/4

    An x-intercept is the value of x where y = 0.  So, from our equation, y = 0 when (x^2 - 3)(x+2)^2 = 0.

    There are three real solutions: x = √3, x = -√3, x = -2

    A y-intercept is the value of y where x = 0.  So, just take the equation and plug-in 0 for x.

    y = [(0^2 - 3)(0 + 2)^2]/[(0 - 3)(0 + 1)(4*0^2 + 3)] = (-3 * 4) / (-3 * 1 * 3) = -12 / -9 = 4/3

Question Stats

Latest activity: earlier.
This question has 1 answers.

BECOME A GUIDE

Share your knowledge and help people by answering questions.