Fill in the Blank 20 points Write the equation of the horizontal asymptote for the function f(x)=(3x^2-6x+1)/(x^2)+5 Be sure you write an equation, not just a number. If there is no horizontal asymptote, type the letters DNE. typeyouranswer

To find the horizontal asymptote of the function $f(x)=\frac {3x^{2}-6x+1}{x^{2}+5}$, we need to compare the degrees of the numerator and denominator.<br /><br />Step 1: Compare the degrees of the numerator and denominator.<br />The degree of the numerator is 2 (since the highest power of x is 2), and the degree of the denominator is also 2.<br /><br />Step 2: Determine the horizontal asymptote.<br />Since the degrees of the numerator and denominator are the same, the horizontal asymptote is given by the ratio of the leading coefficients.<br /><br />The leading coefficient of the numerator is 3, and the leading coefficient of the denominator is 1.<br /><br />Therefore, the equation of the horizontal asymptote is $y=\frac{3}{1}=3$.<br /><br />Answer: $y=3$