Determine the horizontal aymptotes of the function f(x)=3x^2/x^2+1

Answer 1

To determine the horizontal asymptotes of the given function f(x) = 3x^2 / (x^2 + 1), we need to examine the behavior of the function as x approaches positive and negative infinity.

As x approaches positive or negative infinity, the term with the highest degree in the denominator becomes dominant. In this case, the term is x^2.

Since both the numerator and denominator have the same highest degree term (x^2), we can compare their coefficients to determine the horizontal asymptotes.

The coefficient of x^2 in the numerator is 3, while the coefficient of x^2 in the denominator is 1.

Therefore, the horizontal asymptote of the function is y = 3/1, which simplifies to y = 3.

So, the horizontal asymptote of the function f(x) = 3x^2 / (x^2 + 1) is y = 3.