Question

Which functions have a horizontal asymptote at y=0

Answer 1

Functions that have a horizontal asymptote are fractions which have a denominator that is larger than the numerator and a large positive or negative x-value

How can a function that has an asymptote of y = 0 be found?

Functions that have horizontal asymptote at y = 0, are of the form;

$f(x) = \frac{5 \cdot x + 3}{ 3 \cdot {x}^{2} + 1 }$

The characteristics of the above function that gives an asymptote at x = 0 are;

• A function in fraction form

• A denominator that is larger than the numerator

• x is a large positive or negative number

Dividing the above function by x² gives;

$f(x) = \frac{ \frac{5 \cdot x }{ {x}^{2} } + \frac{ 3}{ {x}^{2} } }{ \frac{3 \cdot {x}^{2} }{ {x}^{2} } + \frac{1}{ {x}^{2} } } = \frac{ \frac{5 }{ {x} } + \frac{ 3}{ {x}^{2} } }{ { 3 } + \frac{1}{ {x}^{2} } }$

$y = f(x) = \lim\limits _{x \rightarrow \infty} \frac{ \frac{5 }{ {x} } + \frac{ 3}{ {x}^{2} } }{ { 3 } + \frac{1}{ {x}^{2} } } = \frac{ 0 + 0 }{ { 3 } + 0 } = 0$

Examples of functions that has an asymptote of y = 0 are fractions with a larger denominator than the numerator and large x-value

Learn more about asymptotes of a function here:

https://brainly.com/question/14015917

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