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Natali5045456 [20]
2 years ago
9

Find the horizontal asymptote for y= 5x/x+6 . y = 0 y = −6 none y = 5

Mathematics
2 answers:
gayaneshka [121]2 years ago
5 0

Answer:

y

=

5

x

x

+

6

Find where the expression

5

x

x

+

6

is undefined.

x

=

−

6

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

=

1

m

=

1

Since

n

=

m

, the horizontal asymptote is the line

y

=

a

b

where

a

=

5

and

b

=

1

.

y

=

5

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

=

−

6

Horizontal Asymptotes:

y

=

5

No Oblique Asymptotes

image of graph

olga_2 [115]2 years ago
5 0

Answer:

y = 5

Step-by-step explanation:

Given function:

y=\dfrac{5x}{x+6}

\implies y=5 \left( \dfrac{x}{x+6}\right)

\textsf{As }x \rightarrow +\infty, \  \dfrac{x}{x+6} \rightarrow1  

\implies y\rightarrow5

\textsf{As }x \rightarrow -\infty, \  \dfrac{x}{x+6} \rightarrow1  

\implies y\rightarrow5

As x approaches infinity and negative infinity, y approaches 5 (but never gets there).    Therefore, the horizontal asymptote is y=5

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