What is the horizontal asymptote of the graph of y=3x6−7x+108x5+9x+10?
Answers
Answer:
y
=
3
x
6
−
7
x
+
10
8
x
5
+
9
x
+
10
does not have any horizontal asymptote; however, it has a slant asymptote
y
=
3
8
x
(in green).
Its graph looks like this:
Graph of a slant asymptote.
Graph of a slant asymptote.
Let us look at some details.
lim
x
→
±
∞
3
x
6
−
7
x
+
10
8
x
5
+
9
x
+
10
by dividing by
x
5
,
=
lim
x
→
∞
3
x
−
7
x
4
+
10
x
5
8
+
9
x
4
+
10
x
5
=
±
∞
−
0
+
0
8
+
0
+
0
=
±
∞
Since the limits at infinity do not exist, there are no horizontal asymptotes.y
=
3
x
6
−
7
x
+
10
8
x
5
+
9
x
+
10
does not have any horizontal asymptote; however, it has a slant asymptote
y
=
3
8
x
(in green).
Its graph looks like this:
Graph of a slant asymptote.
Graph of a slant asymptote.
Let us look at some details.
lim
x
→
±
∞
3
x
6
−
7
x
+
10
8
x
5
+
9
x
+
10
by dividing by
x
5
,
=
lim
x
→
∞
3
x
−
7
x
4
+
10
x
5
8
+
9
x
4
+
10
x
5
=
±
∞
−
0
+
0
8
+
0
+
0
=
±
∞
Since the limits at infinity do not exist, there are no horizontal asymptotes.
Step-by-step explanation: