Find the equation for any horizontal asymptotes for the function below.

Ask by Ingram Harmon. in the United States

Mar 22,2025

Question

Find the equation for any horizontal asymptotes for the function below. $$ f(x)=\frac{5-4 x+x^{2}}{7+5 x+4 x^{2}} $$

UpStudy AI · Accepted Answer

Find the horizontal asymptotes for the function $$ f(x)=\frac{5-4x+x^{2}}{7+5x+4x^{2}} $$.
Function by following steps:
- step0: Find the horizontal asymptotes:
  $$f\left(xight)=\frac{5-4x+x^{2}}{7+5x+4x^{2}}$$
- step1: Evaluate the limits $$\lim _{xightarrow +\infty}\left(f\left(xight)ight)$$ and $$\lim _{xightarrow -\infty}\left(f\left(xight)ight):$$
  $$\begin{align}&\lim _{xightarrow +\infty}\left(\frac{5-4x+x^{2}}{7+5x+4x^{2}}ight)\&\lim _{xightarrow -\infty}\left(\frac{5-4x+x^{2}}{7+5x+4x^{2}}ight)\end{align}$$
- step2: Calculate:
  $$\begin{align}&\frac{1}{4}\&\frac{1}{4}\end{align}$$
- step3: The finite values are horizontal asymptotes:
  $$\begin{align}&f\left(xight)=\frac{1}{4}\end{align}$$
The equation for any horizontal asymptotes for the function $$ f(x)=\frac{5-4x+x^{2}}{7+5x+4x^{2}} $$ is $$ f(x)=\frac{1}{4} $$.
The horizontal asymptote for the function $$ f(x)=\frac{5-4x+x^{2}}{7+5x+4x^{2}} $$ is $$ f(x)=\frac{1}{4} $$.

Find the equation for any horizontal asymptotes for the function below.

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