Question

A. Why does the provided equation support the fact that there is a horizontal asymptote of F(x) that is not

Answer 1

Applying limits, it is found that since $a \neq 0, \frac{a}{2} \neq 0$, and hence the horizontal asymptote is not y = 0, thus not being on the x-axis.

The function is given by:

$F(x) = \frac{(ax - 3)(x - 2)}{2(x + 3)(x - 2)}$

The horizontal asymptote is the limit of the function as x goes to infinity, hence:

$y = \lim_{x \rigtharrow \infty} F(x) = \lim_{x \rigtharrow \infty} \frac{(ax - 3)(x - 2)}{2(x + 3)(x - 2)}$

Considering only the terms with the highest exponents:

$y = \lim_{x \rigtharrow \infty} \frac{ax^2}{2x^2} = \frac{a}{2}$

Since $a \neq 0, \frac{a}{2} \neq 0$, and hence the horizontal asymptote is not y = 0, thus not being on the x-axis.

For more on horizontal asymptotes and limits, you can check brainly.com/question/11598999