How do you write a rational function if the asymptotes of the graph are at $x = 3$ $x=3$ and $y = 1$ $y=1$ ?

Question

How do you write a rational function if the asymptotes of the graph are at $x = 3$ $x=3$ and $y = 1$ $y=1$ ?

1 Answer

Impact of this question

4364 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-11T00:07:34

$f (x) = \frac{x}{x - 3}$ $f(x) = x/(x-3)$

Explanation:

Rational functions have vertical asymptotes where the denominator is zero and the numerator is non-zero (or has a zero of lower multiplicity). In our example we want a factor $(x - 3)$ $(x-3)$ in the denominator.

Rational functions have non-zero horizontal asymptotes if the numerator and denominator are of equal degree. The $y$ $y$ value of the asymptote is given by the ratio of the coefficients of the leading terms of the numerator and denominator. In our example we want the leading coefficient of the numerator to be equal to the leading coefficient of the denominator, in order to get an asymptote $y = 1$ $y=1$

So the simplest rational function with the desired behaviour would be:

$f (x) = \frac{x}{x - 3}$ $f(x) = x/(x-3)$

graph{x/(x-3) [-8.5, 11.5, -4.64, 5.36]}

Science

Math

Humanities

... and beyond

How do you write a rational function if the asymptotes of the graph are at $x = 3$ $x=3$ and $y = 1$ $y=1$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you write a rational function if the asymptotes of the graph are at x=3x=3 and y=1y=1?

1 Answer

Explanation:

Related questions

Impact of this question

How do you write a rational function if the asymptotes of the graph are at $x = 3$ $x=3$ and $y = 1$ $y=1$ ?