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Mathematics
Problem
A function
r
r
r
satisfies the following conditions: •
lim
x
→
∞
r
(
x
)
=
3
\displaystyle\lim_{x\to\infty}r(x)=3
x
→
∞
lim
r
(
x
)
=
3
•
lim
x
→
−
∞
r
(
x
)
=
−
1
\displaystyle\lim_{x\to-\infty}r(x)=-1
x
→
−
∞
lim
r
(
x
)
=
−
1
•
r
r
r
has a vertical asymptote at
x
=
1
x=1
x
=
1
Which of the following formulas could define
r
r
r
? a)
4
π
arctan
x
+
1
+
1
x
+
1
\displaystyle \frac{4}{\pi}\arctan x+1+\frac{1}{x+1}
π
4
arctan
x
+
1
+
x
+
1
1
b)
4
π
arctan
x
+
1
\displaystyle \frac{4}{\pi}\arctan x+1
π
4
arctan
x
+
1
c)
4
π
arctan
x
+
1
+
1
x
−
1
\displaystyle \frac{4}{\pi}\arctan x+1+\frac{1}{x-1}
π
4
arctan
x
+
1
+
x
−
1
1
d)
x
+
2
x
−
1
+
2
\displaystyle \frac{x+2}{x-1}+2
x
−
1
x
+
2
+
2
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