Join the IDNLearn.com community and start getting the answers you need today. Our platform offers reliable and detailed answers, ensuring you have the information you need.
Sagot :
Answer:
To find the asymptotes of the graph
=
2
+
1
y=2x+
x
1
, we need to identify where the function behaves in such a way that it approaches infinity or where it is undefined.
Step-by-step explanation:
Vertical Asymptote:
Vertical asymptotes occur where the denominator of a rational function equals zero and the numerator does not simultaneously equal zero (to avoid holes in the graph).
In
=
2
+
1
y=2x+
x
1
:
The vertical asymptote occurs where
=
0
x=0, because the function is undefined at
=
0
x=0 (division by zero).
Horizontal Asymptote:
Horizontal asymptotes describe the behavior of the function as
x approaches positive or negative infinity.
To find the horizontal asymptote:
Compare the degrees of the numerator and the denominator. Since
2
2x (degree 1) grows faster than
1
x
1
(degree -1) as
x approaches infinity or negative infinity, the horizontal asymptote is determined by the leading terms.
Therefore, as
x approaches infinity:
=
2
+
1
≈
2
y=2x+
x
1
≈2x
As
x approaches negative infinity:
=
2
+
1
≈
2
y=2x+
x
1
≈2x
Thus, the horizontal asymptote is
=
2
y=2x.
Summary of Asymptotes:
Vertical asymptote:
=
0
x=0
Horizontal asymptote:
=
2
y=2x
These asymptotes describe the behavior of the function
=
2
+
1
y=2x+
x
1
as
x approaches certain values or infinity.
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Thank you for visiting IDNLearn.com. For reliable answers to all your questions, please visit us again soon.
