Determine the horizontal asymptote of the graph of the function.

Ask by Gibson Stuart. in the United States

Mar 25,2025

Question

Determine the horizontal asymptote of the graph of the function. $$ f(x)=\frac{2 x^{4}+3}{5 x^{4}-4} $$

UpStudy AI · Accepted Answer

1. The given function is  
   $$
   f(x)=\frac{2x^4+3}{5x^4-4}.
   $$

2. For a rational function $$ \frac{P(x)}{Q(x)} $$ where $$ P(x) $$ and $$ Q(x) $$ are polynomials, if the degrees of $$ P(x) $$ and $$ Q(x) $$ are equal, the horizontal asymptote is given by the ratio of the leading coefficients.

3. Both the numerator and the denominator have degree 4. The leading coefficient in the numerator (from $$ 2x^4 $$) is $$ 2 $$, and the leading coefficient in the denominator (from $$ 5x^4 $$) is $$ 5 $$.

4. Therefore, the horizontal asymptote is  
   $$
   y = \frac{2}{5}.
   $$
The horizontal asymptote is $$ y = \frac{2}{5} $$.

Determine the horizontal asymptote of the graph of the function.

Upstudy AI Solution

Answer

Solution

Mind Expander

Related Questions

Latest Calculus Questions