what is the horizontal asymptote of f\left(x\right)=\frac{7x^{2}+5x-2}{2x^{2}-18}
To find the horizontal asymptote of the function f(x), we need to compare the degrees of the numerator and the denominator.
The degree of the numerator is 2 (highest power of x), and the degree of the denominator is also 2.
If the degrees of the numerator and denominator are equal, we can determine the horizontal asymptote by looking at the ratio of the leading coefficients. The leading coefficient is the coefficient of the term with the highest power of x.
For the numerator, the leading coefficient is 7, and for the denominator, the leading coefficient is 2.
Therefore, the horizontal asymptote of f(x) is y = 7/2.