- #1

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**the horisontal assimptote of this function..**

x>0

[tex]

f(x)=|x-1|+\frac{1}{x}\\

[/tex]

for m i get:

m=lim |x-1| +1/x=infinity

x->infinity

so there is no horisontal assimptote here?

Last edited:

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In summary, a vertical asymptote is a vertical line that a function approaches but never crosses. It can occur when the denominator of a rational function becomes zero. To find the vertical asymptote of a function, set the denominator equal to zero and solve for the variable. Knowing the vertical asymptote of a function can help us understand its behavior and identify any discontinuities or restrictions on the domain. A function can have multiple vertical asymptotes when there are multiple values of the variable that make the denominator equal to zero. The difference between a vertical asymptote and a horizontal asymptote is that a vertical asymptote is associated with the behavior of the function near a specific x-value, while a horizontal asymptote describes its behavior for large or small input

- #1

- 1,395

- 0

x>0

[tex]

f(x)=|x-1|+\frac{1}{x}\\

[/tex]

for m i get:

m=lim |x-1| +1/x=infinity

x->infinity

so there is no horisontal assimptote here?

Last edited:

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- #2

Science Advisor

Homework Helper

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- 975

No, there isn't.

A vertical asymptote is a vertical line that a function approaches but never crosses. It can occur when the denominator of a rational function becomes zero.

To find the vertical asymptote of a function, set the denominator equal to zero and solve for the variable. The resulting value is the x-coordinate of the vertical asymptote.

Knowing the vertical asymptote of a function can help us understand the behavior of the function as the input values get closer and closer to the asymptote. It also helps us identify any discontinuities or restrictions on the domain of the function.

Yes, a function can have multiple vertical asymptotes. This can occur when there are multiple values of the variable that make the denominator of the function equal to zero.

A vertical asymptote is a vertical line that the function approaches but never crosses, while a horizontal asymptote is a horizontal line that the function approaches as the input values get larger or smaller. A vertical asymptote is associated with the behavior of the function near a specific x-value, while a horizontal asymptote describes the behavior of the function for large or small input values.

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