r(x) Suppose p/q is a rational function where the degree of p is 1 greater than the degree of q. Using polynomial long division, p/q can be written as = mx + b + where r/s is a rational function with the property s(x) p(x) q(x) p(x) r(x)/(x)→0 as x→ +∞o. This fact implies that (x) O A. The vertical asymptote of f is x = OB. There are no vertical asymptotes. x²-x+7 3x - 1 mx + b when x is large. The line y = mx + b is an oblique (or slant) asymptote of p/q. Complete parts (a) through (c) for the function f(x) = (b) Find the vertical asymptote of f. Select the correct choice below, and, if necessary, fill in the answer box to complete your choice. Q Q (Type an integer or a fraction.) (c) Graph f and all of its asymptotes with a graphing utility. Choose the correct graph below. O A. O B. Ju The window setting for all graphs is [-6, 6,1] by [-6,6,11. • Q Q O C. O D. Q

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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p(x)
Suppose p/q is a rational function where the degree of p is 1 greater than the degree of q. Using polynomial long division, p/q can be written as = mx + b + where r/s is a rational function with the property
q(x)
r(x)
s(x)
p(x)
r(x)/s(x)→0 as x→ +∞o. This fact implies that
q(x)
(b) Find the vertical asymptote of f. Select the correct choice below, and, if necessary, fill in the answer box to complete your choice.
OA. The vertical asymptote of f is x =
OB. There are no vertical asymptotes.
x²-x+7
mx + b when x is large. The line y = mx + b is an oblique (or slant) asymptote of p/q. Complete parts (a) through (c) for the function f(x) =
3x - 1
O A.
(Type an integer or a fraction.)
(c) Graph f and all of its asymptotes with a graphing utility.
Choose the correct graph below.
OB.
The window setting for all graphs is [-6, 6, 1] by [-6,6,11.
Q
O C.
H.
O D.
Transcribed Image Text:p(x) Suppose p/q is a rational function where the degree of p is 1 greater than the degree of q. Using polynomial long division, p/q can be written as = mx + b + where r/s is a rational function with the property q(x) r(x) s(x) p(x) r(x)/s(x)→0 as x→ +∞o. This fact implies that q(x) (b) Find the vertical asymptote of f. Select the correct choice below, and, if necessary, fill in the answer box to complete your choice. OA. The vertical asymptote of f is x = OB. There are no vertical asymptotes. x²-x+7 mx + b when x is large. The line y = mx + b is an oblique (or slant) asymptote of p/q. Complete parts (a) through (c) for the function f(x) = 3x - 1 O A. (Type an integer or a fraction.) (c) Graph f and all of its asymptotes with a graphing utility. Choose the correct graph below. OB. The window setting for all graphs is [-6, 6, 1] by [-6,6,11. Q O C. H. O D.
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