Final answer:
The vertical asymptotes do not exist for the function, while the horizontal asymptote is y = 9/4.
Step-by-step explanation:
To determine the vertical and horizontal axes of the function F(x) = (9x² - 5) / (4x² + 6), we need to look at the degree of the numerator and denominator polynomials. In this case, the degree of the numerator is 2 and the degree of the denominator is also 2. Therefore, the vertical asymptotes of the function occur where the denominator is equal to zero. Setting 4x² + 6 = 0, we find that x² = -3/2, which is not possible since the square of any real number cannot be negative. Hence, there are no vertical asymptotes for this function.
However, we can determine the horizontal asymptote by comparing the degrees of the numerator and denominator polynomials. Since the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote can be found by dividing the leading coefficients of the polynomials. In this case, the leading coefficients are both 9 and 4. Therefore, the horizontal asymptote is y = 9/4.