What are the vertical asymptotes of 10/X-1​

Answer:

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Algebra Examples

Popular Problems Algebra Find the Asymptotes f(x)=10/(x^2-1)

f

(

x

)

=

10

x

2

−

1

Find where the expression

10

x

2

−

1

is undefined.

x

=

−

1

,

x

=

1

Since

10

x

2

−

1

→

∞

as

x

→

−

1

from the left and

10

x

2

−

1

→

−

∞

as

x

→

−

1

from the right, then

x

=

−

1

is a vertical asymptote.

x

=

−

1

Since

10

x

2

−

1

→

−

∞

as

x

→

1

from the left and

10

x

2

−

1

→

∞

as

x

→

1

from the right, then

x

=

1

is a vertical asymptote.

x

=

1

List all of the vertical asymptotes:

x

=

−

1

,

1

Consider the rational function

R

(

x

)

=

a

x

n

b

x

m

where

n

is the degree of the numerator and

m

is the degree of the denominator.

1. If

n

<

m

, then the x-axis,

y

=

0

, is the horizontal asymptote.

2. If

n

=

m

, then the horizontal asymptote is the line

y

=

a

b

.

3. If

n

>

m

, then there is no horizontal asymptote (there is an oblique asymptote).

Find

n

and

m

.

n

=

0

m

=

2

Since

n

<

m

, the x-axis,

y

=

0

, is the horizontal asymptote.

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

=

−

1

,

1

Horizontal Asymptotes:

y

=

0

No Oblique Asymptotes

image of graph

The vertical asymptotes of the given function are x = 1 and x = -1,

We have given the rational function is 10/(x²-1​).

We need to find the vertical asymptotes of this function.

Since Vertical asymptotes occur when the denominator of the function becomes zero and the numerator is not zero.

To determine the vertical asymptotes of the function, we need to solve the denominator for x²-1=0.

x²-1=0

x²=1

x=±√1

x=±1

Therefore, the vertical asymptotes of the given function are x = 1 and x = -1, since the denominator becomes zero at x=1 and x=-1.

To learn more about vertical asymptotes visit:

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