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Find the horizontal and vertical asymptotes of the graph of the function. (You need not sketch the graph. If an answer does not exist, enter DNE.)g(x) = (6 x)/(x^2 + 10 x - 24)

Question

Find the horizontal and vertical asymptotes of the graph of the function. (You need not sketch the graph. If an answer does not exist, enter DNE.)
g(x) = (6 x)/(x^2 + 10 x - 24)

check_circleAnswer
Step 1

Given,

6 x
g(x)
х2+ 10 х - 24
For vertical asymptotes
Zeros of the denominator are the vertical asymptotes
x210 x 24 = 0
х2 + 12 х — 2х - 24 — 0
х(х + 12) — 2( х+ 12) — 0
(х + 12)( х — 2) %3D 0
-12 or x 2
Either x
So, vertical asymptotes: x = -12 and x = 2
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6 x g(x) х2+ 10 х - 24 For vertical asymptotes Zeros of the denominator are the vertical asymptotes x210 x 24 = 0 х2 + 12 х — 2х - 24 — 0 х(х + 12) — 2( х+ 12) — 0 (х + 12)( х — 2) %3D 0 -12 or x 2 Either x So, vertical asymptotes: x = -12 and x = 2

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Step 2

For horizontal a...

6х
6
lim
x00 x210 x - 24
lim
x0o x 10
= 0
24
х
6х
6
lim
x00 x2+10 x - 24
lim
= 0
24
х+-0о х+ 10
x
So, horizontal asymptotes: y = 0
help_outline

Image Transcriptionclose

6х 6 lim x00 x210 x - 24 lim x0o x 10 = 0 24 х 6х 6 lim x00 x2+10 x - 24 lim = 0 24 х+-0о х+ 10 x So, horizontal asymptotes: y = 0

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Calculus

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