How do you identify the vertical and horizontal asymptotes for rational functions?

bolton8l
2022-09-03
Answered

How do you identify the vertical and horizontal asymptotes for rational functions?

You can still ask an expert for help

Johnny Parrish

Answered 2022-09-04
Author has **12** answers

How to Find Horizontal Asymptotes of Rational Functions

Let $f\left(x\right)=\frac{p\left(x\right)}{q\left(x\right)}$, where p(x) is a polynomial of degree m with leading coefficient a, and q(x) is a polynomial of degree n with leading coefficient b. There are three cases:

Case 1: If m>n, then f has no horizontal asymptotes.

Case 2: If m=n, then $y=\frac{a}{b}$ is the horizontal asymptote of f.

Case 3: If m

How to Find Vertical Asymptotes of Rational Functions

If there are any common factors between the numerator and the denominator, then cancel all common factors. Set the denominator equal to zero then solve for x.

Let $f\left(x\right)=\frac{p\left(x\right)}{q\left(x\right)}$, where p(x) is a polynomial of degree m with leading coefficient a, and q(x) is a polynomial of degree n with leading coefficient b. There are three cases:

Case 1: If m>n, then f has no horizontal asymptotes.

Case 2: If m=n, then $y=\frac{a}{b}$ is the horizontal asymptote of f.

Case 3: If m

How to Find Vertical Asymptotes of Rational Functions

If there are any common factors between the numerator and the denominator, then cancel all common factors. Set the denominator equal to zero then solve for x.

asked 2021-02-25

True or False. The graph of a rational operate could encounter a horizontal straight line.

asked 2022-07-10

This integral poses a challenge.

Ordinarily integrating rational functions can be solved using the Hermite-Ostrogradski method. However, in the following integral, the coefficients ${\beta}_{0},...,{\beta}_{4}$ are not integers. (Hence, the Hermite-Ostrogradski method would not be appropriate).

Note: Expanding the integrand (trying to solve the integral using a partial fraction decomposition) is (because of the nature of the physical problem described by this integral) an inappropriate solution to this case.

$\int {\displaystyle \frac{1}{{\beta}_{0}+{\beta}_{1}x+{\beta}_{2}{x}^{2}+{\beta}_{3}{x}^{3}+{\beta}_{4}{x}^{4}}}dx$

How can this rational function be evaluated?

Ordinarily integrating rational functions can be solved using the Hermite-Ostrogradski method. However, in the following integral, the coefficients ${\beta}_{0},...,{\beta}_{4}$ are not integers. (Hence, the Hermite-Ostrogradski method would not be appropriate).

Note: Expanding the integrand (trying to solve the integral using a partial fraction decomposition) is (because of the nature of the physical problem described by this integral) an inappropriate solution to this case.

$\int {\displaystyle \frac{1}{{\beta}_{0}+{\beta}_{1}x+{\beta}_{2}{x}^{2}+{\beta}_{3}{x}^{3}+{\beta}_{4}{x}^{4}}}dx$

How can this rational function be evaluated?

asked 2022-09-12

How do you graph $f\left(x\right)=\frac{x}{{x}^{2}+x-2}$ using holes, vertical and horizontal asymptotes, x and y intercepts?

asked 2022-08-31

If y varies inversely with x and y = 8 when x = 5, then what is y when x = 2?

asked 2022-09-04

Which is the quadratic variation equation for the relationship given y varies directly with x^2 and y = 36 when x = 3?

asked 2021-06-27

Graph the rational functions. Include the graphs and equations of the asymptotes and dominant terms. $y=\frac{1}{2x+4}$

asked 2022-02-18

I'm trying to find out under which conditions does a sum of a rational function $\sum f\left(n\right)$ converges, with $f\left(x\right)=\frac{A\left(x\right)}{B\left(x\right)}$ , with $degB>degA$ and $\mathrm{\forall}X,B\left(X\right)\ne 0$ .

Who knows?

Who knows?