Find where the expression
x
−
5
x
2
−
25
x
-
5
x
2
-
25
is undefined.
x
=
−
5
,
x
=
5
x
=
-
5
,
x
=
5
Since
x
−
5
x
2
−
25
x
-
5
x
2
-
25
→
→
−
∞
-
∞
as
x
x
→
→
−
5
-
5
from the left and
x
−
5
x
2
−
25
x
-
5
x
2
-
25
→
→
∞
∞
as
x
x
→
→
−
5
-
5
from the right, then
x
=
−
5
x
=
-
5
is a vertical asymptote.
x
=
−
5
x
=
-
5
Consider the rational function
R
(
x
)
=
a
x
n
b
x
m
R
(
x
)
=
a
x
n
b
x
m
where
n
n
is the degree of the numerator and
m
m
is the degree of the denominator.
1. If
n
<
m
n
<
m
, then the x-axis,
y
=
0
y
=
0
, is the horizontal asymptote.
2. If
n
=
m
n
=
m
, then the horizontal asymptote is the line
y
=
a
b
y
=
a
b
.
3. If
n
>
m
n
>
m
, then there is no horizontal asymptote (there is an oblique asymptote).
Find
n
n
and
m
m
.
n
=
1
n
=
1
m
=
2
m
=
2
Since
n
<
m
n
<
m
, the x-axis,
y
=
0
y
=
0
, is the horizontal asymptote.
y
=
0
y
=
0
There is no oblique asymptote because the degree of the numerator is less than or equal to the degree of the denominator.
No Oblique Asymptotes
This is the set of all asymptotes.
Vertical Asymptotes:
x
=
−
5
x
=
-
5
Horizontal Asymptotes:
y
=
0
y
=
0
No Oblique Asymptotes
It’s is 1)
A black kid black white white shirt with green green red black
5k in miles is 3.10686 miles
Answer:
(use algebra) 1st no. is a,2nd no. is 8 times the 1st which is 8a, 3rd no. 100 more than 1st which is a+100
total is 420, thus a+8a+a+100=420
10a+100=420, take 100 to the other side
10a=320 hence 32
1st no. is 32, 2nd is 256, 3rd is 356
