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Question 1039074: I could use some help on this one. I really appreciate it!
Let f(x) = 6x^2 - 24 / x^2 - 36
(a) State the y-intercept.
(b) State the x-intercept(s).
(c) State the vertical asymptote(s).
(d) State the horizontal asymptote.
Thank you so much for your help!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Let f(x) = 6x^2 - 24 / x^2 - 36
(a) State the y-intercept.
Let x = 0, then
f(0) = -24/-36 = 2/3 ; (that is the y-intercept)
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(b) State the x-intercept(s).
Let y = 0, then
(6x^2-24)/(x^2-36) = 0
6x^2 - 24 = 0
6(x^2-4) = 0
x^2-4 = 0
x = 2 or x = -2
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(c) State the vertical asymptote(s).
Solve x^2-36 = 0
(x-6)(x+6) = 0
x = 6 or x = -6
Those are the VA's
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(d) State the horizontal asymptote.
y = 6x^2/x^2 = 6
That is the HA.
Cheers,
Stan H.
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