Identify the horizontal asymptote of f(x) =3/5x

Question

05-02-2018
Mathematics

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Identify the horizontal asymptote of f(x) =3/5x

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kudzordzifrancis kudzordzifrancis · Answer 1 · 2018-12-02T08:39:23+01:00

ANSWER

The horizontal asymptote is
[tex]y = 0[/tex]

EXPLANATION

The given function is
[tex]f(x) = \frac{3}{5x} [/tex]

This is a rational function which can be rewritten as,

[tex]f(x) = \frac{0x + 3}{5x} [/tex]

The horizontal asymptote can be found by expressing the coefficient of
[tex]x[/tex]

in the numerator over the coefficient of
[tex]x[/tex]
in the denominator.

Thus the horizontal asymptote is,
[tex]y = \frac{0}{5} [/tex]
This simplifies to
[tex]y = 0[/tex]

Therefore the horizontal asymptote of the given rational function coincides with the x-axis.

It is the red straight line in the attachment.

lublana lublana · Answer 2 · 2019-11-28T05:37:33+01:00

Answer:

y=0

Step-by-step explanation:

We are given that a rational function

[tex]f(x)=\frac{3}{5}x[/tex]

We have to find the horizontal asymptote of the given function.

The function can be written as

[tex]f(x)=\frac{3x^0}{5x}[/tex]

Degree of numerator polynomial=0

Degree of denominator polynomial=1

Degree of numerator polynomial is less than the degree of denominator polynomial.

When degree of numerator polynomial is less than the degree of denominator polynomial then,

Horizontal asymptote=y=0

Therefore, horizontal asymptote=0