Find the horizontal asymptote, if any, of the graph of the given function.
g(x) = 4x^5+9x^4+1/9x^5+3x^4-9x^2+3x+1
To find the horizontal asymptote of a function, we need to examine what happens to the function as x approaches positive infinity and negative infinity.
In this particular case, we can determine the horizontal asymptote by comparing the degree of the numerator and the degree of the denominator of the rational function g(x).
Looking at the exponent of the highest power of x in both the numerator (5) and denominator (5), we can conclude that the degree of the function is equal in both the numerator and denominator.
In this scenario, we can find the horizontal asymptote by dividing the coefficient of the highest power of x in the numerator by the coefficient of the highest power of x in the denominator.
For g(x) = 4x^5+9x^4+1/(9x^5+3x^4-9x^2+3x+1), the coefficient of the highest power of x in the numerator is 4, and the coefficient of the highest power of x in the denominator is 9.
Dividing 4 by 9, we find that the horizontal asymptote is y = 4/9.
Therefore, the horizontal asymptote of the graph of g(x) is y = 4/9.