Question
Find all horizontal and vertical asyinptoles of
.
Find the horizontal asymptotes. Select the correct choice and, if necessary, fill in the answer box(es) to complete your choice.
A. The function has one horizontal asymptote,
,
(Type an equation.)
B. The function has two horizontal asymptotes. The top asymptote is
and the bottorn asymplote is
(Type equations.)
Find the vertical asymptotes. Select the correct choice and, if necessary, fill in the answer box(es) to complete your choice.
A. The function has one vertical asymptote,
.
(Type an equation.)
B. The function has two vertical asymptotes. The leltriost asymptote is
and the nightmost asymptole is
(Type equations)
C. The function has no vertical asymptotes.
Find the horizontal asymptotes. Select the correct choice and, if necessary, fill in the answer box(es) to complete your choice.
A. The function has one horizontal asymptote,
(Type an equation.)
B. The function has two horizontal asymptotes. The top asymptote is
(Type equations.)
Find the vertical asymptotes. Select the correct choice and, if necessary, fill in the answer box(es) to complete your choice.
A. The function has one vertical asymptote,
(Type an equation.)
B. The function has two vertical asymptotes. The leltriost asymptote is
(Type equations)
C. The function has no vertical asymptotes.
Ask by Barker Cook. in the United States
Jan 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Horizontal Asymptote:
Vertical Asymptotes:
and
Solution

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The Deep Dive
To find the horizontal asymptotes of the function
, we start by noting the degrees of the numerator and the denominator. Both the numerator and denominator have a degree of 2. The horizontal asymptote is determined by the coefficients of the leading terms. Here, the leading coefficient of the numerator is 4 and that of the denominator is 1, so
. Thus, the correct choice is:
A. The function has one horizontal asymptote,
.
Next, for the vertical asymptotes, we need to find where the denominator equals zero, as these points typically indicate vertical asymptotes. The denominator is
. Factoring this expression gives us
, which means
and
are the locations of the vertical asymptotes. So, the correct choice is:
B. The function has two vertical asymptotes. The leftmost asymptote is
and the rightmost asymptote is
.